It would be "desirable" to legislate for more powers for Holyrood in the first year of the first parliament after a No vote, according to the Prime Minister.

David Cameron said he sees no reason why the move could not happen "very early" in the next Westminster parliament, but stopped short of making a specific pledge on the timings.

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The Prime Minister's comments came a day after a visit to Glasgow in which he vowed to deliver more powers for the Scottish Parliament if the country votes to remain in the UK.

"It's very important if you want further devolution, the way to get it is a No vote," he said.

Mr Cameron today insisted it is a "strong" promise.

"What's interesting is that all the political parties that support the United Kingdom staying together, Labour, Liberal Democrats and Conservatives, all believe there are opportunities for further devolution," he told BBC Radio Scotland.

The Prime Minister pointed to his record on delivering further powers, saying the Scotland Act represented an "enormous act of devolution strengthening the Scottish Parliament".

He told the Good Morning Scotland programme: "There's a strong track record there. Obviously people want to be certain it will happen and I would say it happened in this parliament, if I'm Prime Minister in the next parliament it will happen in the next parliament.

"I don't see any reason why it shouldn't happen very early in the parliament. The only reason I haven't given a specific pledge is each of the parties has got to set out their plans, we need to have a general election, we need to see the result of that election and then if I was prime minister I'd want to try and proceed as I have done so far on the basis of building consensus."

The Prime Minister did not give details about what the further powers could be.

But when asked if he was talking about legislating in the first year of a second term, he said: "If that was possible then that would be obviously desirable.

"The only reason I haven't given a specific pledge is as I say, I think you need to seek agreement between the parties so that what you put forward has the broadest possible support in Scotland."

Speaking just days ahead of the European Parliament elections, the Prime Minister argued that Scots want an in/out referendum on membership of the EU.

He said: "I hope Scotland will stay in the United Kingdom because we are better together and I hope the United Kingdom will stay in a reformed European Union, but it's time we were given a choice about our European future and I'm the only Prime Minister and politician who can guarantee that because we will hold an in/out referendum by the end of 2017 if I'm prime minister after the next election.

"The interesting thing is that in Scotland there's a majority of people who want to see that reform of the European Union, who want to see that referendum. So it's not just the right thing to do for Britain, I think it also has the support of the people."

He went on: "When you look at the figures, actually a majority of Scots do support having the choice of an in/out referendum.

"When you run through the options: stay in the EU unamended; leave the EU straight away; or seek changes and then stay in a reformed EU - it's that latter choice that's the most popular amongst Scots."

Mr Cameron is continuing his visit to Scotland today to make "the positive arguments in favour of Scotland remaining part of the UK".

He is speaking to young people in the south of the country to discuss the referendum on the final day of a two-day trip north of the border.

Scottish First Minister Alex Salmond has said people will not believe promises of further devolution and has reiterated calls for a debate with the Prime Minister on independence.

He said: ''The Prime Minister is perfectly entitled to come to Scotland, and we are perfectly entitled to ask why he isn't prepared to have a debate in Scotland. He is prepared to have a debate with Ukip and the Greens, but not on the future of Scotland.

''If you are entering a debate, you cannot be half in that debate - you have to be accountable, which is why he should agree to a one-to-one TV debate, First Minister to Prime Minister.''

The Prime Minister visited Lockerbie Ice Rink, Dumfriesshire, this morning to speak to local high school children.

Lockerbie Academy recently voted 70% in favour of remaining in the UK in a mock referendum.

Senior pupils will get a chance to vote in a major poll for the first time after the Scottish Government extended the voting franchise to 16 and 17-year-olds.

Mr Cameron urged Scots to vote No to prevent their nation becoming "a foreign country".

"Of course I am deeply concerned that we get the right result," he told ITV Border.

"Alex Salmond is making an extraordinary argument. London is an enormous and precious asset for the whole of the UK, and many Scots benefit from London's hub status and from working and investing in London and from the investment from London into Scotland.

"Now surely we should be making the most out of that connectivity rather than separating ourselves from it.

"People in Scotland say to me 'I've got children working or studying in London', and people in London say to me 'I've got children working or studying in Scotland'. Do we really want to have a situation where they are working or studying in a foreign country?

"We don't want that so let's not vote for it, let's vote to keep the UK together."

He once again rejected Mr Salmond's demand for a TV debate.

"I know why Alex Salmond wants to have a debate, it's because he's losing on the issues about jobs, prosperity and security, so he wants to have a debate between what he would see as a Scottish nationalist against an English Tory as he would call it, and it would be a wonderful distraction for him."

Mr Cameron also reiterated his claim that Scotland would lose the pound if it voted for independence.

"The head of the UK Treasury and the governor of the Bank of England have been clear that for Scotland you keep the pound as part of the UK but if you leave the UK you lose the pound," he said.

"I'm pretty clear about when a governor of the Bank of England says difficult - I'll leave him to speak for himself - but the argument I am putting is that Scotland keeps the pound inside of the UK but doesn't outside of the UK.

"That is not simply the view of the political leaders in the Labour, Liberal Democrat and Conservative parties, it's also the view of experts who have been advising us."