Speaking shortly after the face-to-face talks in Edinburgh, Mr Cameron said his "absolute priority" was to preserve the United Kingdom.
He said that voters in Scotland should be presented as soon as possible with a "simple, straightforward and legal" question over whether they want to remain in the UK or not.
And he held out the prospect of further talks on increased devolution of powers if Scotland votes to remain in the Union.
Mr Cameron described his discussions with Mr Salmond as "constructive", but said: "On the issue of independence, separating Scotland, leaving the United Kingdom, I am afraid there wasn't much progress.
"I believe that we need to put a straightforward and simple and legal question to the Scottish people in good time, which is to ask the straightforward question 'Do you want to stay in the United Kingdom...' - and I hope that is what people will vote for - '... or do you want to leave the United Kingdom?"'
Mr Cameron added: "If the answer to the question is that Scotland wants to stay in the United Kingdom, then further options for devolution are on the table.
"We can discuss those just as we have in the past, to make sure that all the parts of the United Kingdom feel that they get a good deal inside the United Kingdom.
"My absolute priority is to keep the United Kingdom together. It has worked for all our countries, it's made us safer, it's made us stronger, it's made us richer, it's helped us in times of difficulty. We shouldn't give up this great thing - our United Kingdom."
After the meeting, Mr Salmond said it was now incumbent on Mr Cameron and others to set out more details on the offer of further devolution for Scotland.
Mr Salmond said: "The Prime Minister is now saying for the first time that another option is now on the table. What I said to the Prime Minister in the discussions is if that is the case, we now have to know what it will be."
He said "we've been through this before in Scottish politics", recalling that in the run-up to the 1979 referendum, Sir Alec Douglas-Home had said a Tory government would introduce a better Scottish Assembly.
But Mr Salmond said: "What happened then was 17, 18 years of no deal at all from the Conservative government at Westminster."
The First Minister added: "The shadow of Sir Alec Douglas-Home I think is cast very large over this. What's the old saying 'fool me once, shame on you, fool me twice shame on me'. Scotland, I don't believe, will be fooled twice."
Mr Salmond also insisted that the main "stumbling block" in terms of the process of staging the referendum hinged on the issue of whether there should be one or two questions put to voters.
The UK Government wants Scots to be given a straight choice between independence and staying in the United Kingdom.
However, Mr Salmond's SNP administration is open to also giving voters the option of backing further powers for Holyrood, an issue which is included in its consultation on the referendum.
The First Minister said: "The Prime Minister's position is he wants to have one question. My position is we are in the middle of a consultation with the Scottish people and we are open-minded. If there is a strong demand from civic Scotland, from the unions, the voluntary sector, the churches, civic society in Scotland, for something different, for some other option to be tested, politicians at the very least should listen to that."
And while Mr Salmond said he had not reached an agreement with Mr Cameron, he said that "things have moved on quite substantially".
Mr Salmond highlighted the "emergence that something else might be on offer on the table" and stated: "Although there isn't agreement I think things have moved on quite substantially."
As well as discussing the independence referendum with Mr Cameron today, the First Minister held talks on the issue with Scottish Secretary Michael Moore on Monday. Following those, the SNP leader highlighted the issue of whether or not 16 and 17-year-olds should get to vote in the ballot as one area where the Scottish Government disagreed with Westminster.
Mr Moore - who was also present at today's talks - later said the timing of the ballot was also an issue, as he called for the referendum to take place sooner than the Nationalists' preferred timetable of autumn 2014.
Today, Mr Salmond said he believed the "only really substantive sticking point, point of disagreement, which hasn't been resolved, is one or two questions".
He added: "I think there's differences of opinion on other matters, but they are not differences of opinion that are not capable of resolution."
The First Minister also demanded that details of the Prime Minister's offer of further devolution be spelled out "urgently" in the next few months.
He pointed out Westminster politicians had been calling for the referendum to be sooner rather than later and said: "There's something contradictory about people saying we want a very quick debate on this but they don't actually have their option at all worked out."
He added: "I now say to the anti-independence parties, particularly the senior member of the coalition in London, give us the detail, where's the beef, what is the proposal, what is on the table?
"Is it not rather more than cheeky for people who want a referendum the day after tomorrow to come up this morning with something on the table, but they haven't specified what it is?"
After the discussions, Mr Moore told journalists that any further powers for Scotland can be debated after the referendum.
"The alternative is not the status quo, it's actually about deciding what other powers Scotland should have within the United Kingdom," he said.
"If I may speak as a Liberal Democrat, we have the Home Rule Commission set up by Willie Rennie, our Scottish leader, that's looking at exactly those issues. So there isn't a blueprint, there are some principles, some issues and some areas we can examine.
"We don't need the outcome of a referendum to determine whether or not we can have the debate about what those powers will be. For the Liberal Democrats, we are under way with that debate. I anticipate that other parties, and frankly those of no party in Scotland, will also be part of that debate.
"That will be judged and determined separately from this central, fundamental question about the future of Scotland's place in the UK."
He attempted to turn the question on Mr Salmond, arguing that there is a lack of detail on what independence means. Mr Moore added: "We keep seeing a moving feast from the SNP on what that might look like.
"We've seen a shift on the currency the country might adopt. We have had very little clarity about how we would do very major things like regulating our banks and financial institutions. We've had precious little detail about what we would do about negotiating our way back into the European Union, or what our membership of Nato, or not, would mean for Scotland.
"There are a whole range of issues there about independence, the central areas of debate that have not yet been resolved."
He rejected suggestions that the position on the future of devolution undermines the current proposals going through Westminster in the Scotland Bill. "I've never noticed the debate on devolution stopping," he said.
The Lib Dems are due to discuss the issues at their Scottish conference in Inverness next month, he added. "The independence referendum is now on," he said.
"Let's not complicate things or confuse matters, make a muddle of this, by having two questions. Let's just deal with the central issue."
Earlier, the Prime Minister used a speech in Edinburgh to set out his defence of more than 300 years of political union between Scotland and England.
Read the speech in full here
In his keynote speech, Mr Cameron acknowledged that Scotland - and England - could make their ways as independent states, but said he was "convinced" the UK's best days lay ahead.
Mr Cameron said: "I come here today with one simple message: I hope and wish that Scotland will vote to remain part of the United Kingdom."
Describing the UK as more than "some sort of deal", he added: "It's a precious thing. It's about our history, our values, our shared identity and our joint place in the world ...
"From Waterloo to the Second World War, our servicemen and women have fought and won together ... Your heroes are our heroes."
Mr Cameron said his part in the constitutional debate was not motivated by party interest, acknowledging the sole Tory MP north of the border.
"I know the Conservative Party isn't currently - how can I put this? - Scotland's most influential political movement," he said.
"I'm often reminded that I've been more successful in getting pandas to the zoo than Conservative MPs elected in Scotland. So, more than a little humility is called for when any contemporary Tory speaks in Scotland. In fact, some say it might be wiser not to speak at all."
But he rejected calls from his own party that Scottish independence would make it easier for Tories to get a majority at Westminster. "That doesn't interest me. I'm not here to make a case on behalf of my party, its interests or its approach to office," he said.
Mr Cameron conceded that pro-union politicians needed to do more get their message out to voters and suggested he hoped Labour's Alistair Darling and Gordon Brown would get involved.
"My voice is just one of those voices. You will see Labour politicians, Liberal Democrat politicians, and indeed people from all walks of life - and many people who don't like politics at all - who will come forward and defend the United Kingdom.
"Do we need to do more? Yes. Do we need those who care about the United Kingdom to work together? Yes. Do we need to galvanise opinion across the country? Yes. But is that opinion there to be galvanised? Absolutely."
Earlier, Mr Cameron toured the Quaker Oats factory in Cupar, Fife, on the day it announced a £14.4 million investment and 30 new jobs at the site.
Pressed on whether his privileged background would deter Scottish voters from backing the pro-union campaign, he said: "As for the fact that I am English, that I had a privileged upbringing, that I might annoy people by making a speech in Scotland, all I can say is that this is what I believe. I care about our United Kingdom."