There is "no question" that Mr Salmond will debate with Better Together chief Alistair Darling and Scottish Secretary Alistair Carmichael between now and the referendum, Ms Sturgeon said.
But Ms Sturgeon reiterated that the First Minister's main target is Prime Minister David Cameron whom Mr Salmond has repeatedly lobbied to take part in a live televised debate.
Ms Sturgeon did not say whether the debates with Mr Darling and Mr Carmichael would be televised.
She said: "I am sure that between now and the referendum Alex Salmond will debate with both of those people and many others, making the positive case for independence. There is no issue or question about that.
"The real question is why will David Cameron not agree to debate with Alex Salmond? What is he running scared of? That is the unanswered question.
"I've already debated with Alistair Darling. I've debated with Michael Moore. Alex Salmond will debate with lots of people between now and the referendum, but the first and foremost point here is that there should be that debate between the First Minister and the Prime Minister.
"Alex Salmond wants to debate the Prime Minister. I think that's right and proper. This is a debate about a transfer of powers from Westminster to the Scottish Parliament. Surely it's right and proper that the leader of the Scottish Government debates with the leader of the UK Government."
Better Together claimed Ms Sturgeon's comments are a "U-turn".
A spokesman said: "It is good news that Nicola Sturgeon has finally confirmed that Alex Salmond has backed down and will now have a live TV debate with Alistair Darling. Now that both sides have agreed, it's time for the campaigns to get on and make this happen."
Meanwhile, Mr Salmond claimed a "natural majority" of people in Scotland are in favour of independence.
More voters trust the Scottish Government to make the best decisions for Scotland than those who trust "a Westminster system that rarely represents the votes or the values of the Scottish people".
That trust will lead to a Yes vote in next year's independence referendum, he said.
Mr Salmond, addressing the opening day of the SNP annual conference in Perth, described the referendum as a "date with destiny" and the "biggest opportunity that Scotland has ever had".
In the coming year, the SNP will "focus on the real debate" of "who can be trusted to make the best decisions for Scotland", he said.
"By a factor of four to one, people trust the Scottish Government rather than the Westminster Government to govern Scotland. And they believe Scotland's Parliament should make the key decisions on tax, on welfare, on pensions.
"That is the natural majority for Scottish independence. It exists in this land at the moment and it is why I believe it will be reflected in a majority for Yes in the ballot paper next September."
A Yes vote will be chosen "for hope, rather than the fear offered by the No campaign", he said.
"One of the reasons I've got for believing that is no one actually really now believes that Scotland has not got what it takes to be an independent country."
Mr Salmond said those campaigning against independence branded themselves "Project Fear" and "internal tensions" could surface among those fighting to keep Scotland in the UK.
"At heart, the No campaign and the key people in it don't deny the economic viability or the potential of people in talented, resource-rich Scotland. Nobody could actually argue that this country doesn't have what it takes to in terms of people, in terms of resources.
"When even the bitterest opponents of Scottish independence agree Scotland has got what it takes, the only thing people have to fear is Project Fear itself."
Delegates later backed resolutions on the "appalling" need for food banks and supporting an end to Trident nuclear weapons.
SNP defence spokesman Angus Robertson said: "It is shameful that people are having to use food banks to feed their children and their families, and it is an outrage that the decision-makers in London have decided that it is a better use of money to spend it on Trident armed submarines that will never be used in any circumstances.
"This, of all subjects, reflects the reason why we need that Yes vote."
In an interview with Channel 4 this week, US investigative journalist Eric Schlosser spoke about difficulties in obtaining information from the Ministry of Defence on Trident nuclear safety issues.
Referring to Mr Schlosser's comments, Mr Robertson added: "We have yet another reason to understand why you should not have weapons of mass destruction just a few miles down the Clyde from Scotland's largest city."
MSP Bill Kidd said it was possible there could be a nuclear accident at the Faslane Trident base. "That is not scaremongering, that is fact," he said.
He told delegates that Mr Schlosser's comments were "a new worrying concern".
"Westminster is secretive about Trident, because Westminster has reason to be secretive.
"But we are transparent about Trident - it will not continue to exist in an independent Scotland."