David Cameron has agreed to meet Alex Salmond to discuss plans for a referendum on Scottish independence.
Downing Street said arrangements for the meeting between the Prime Minister and First Minister would be made "in the coming days".
However, the Prime Minister also put pressure Mr Salmond to accept Scottish Secretary Michael Moore's invitation for a meeting in Edinburgh on Thursday.
Mr Salmond has indicated he would prefer to discuss the two government's differences directly with the Prime Minister.
Deputy Prime Minister Nick Clegg will also meet the First Minister.
A Number 10 spokesman said: "The Prime Minister has made it clear he is happy to meet Alex Salmond and arrangements for that will be made in the coming days.
"However, he also believes the First Minister should accept the invitation to meet the Secretary of State for Scotland on Thursday to discuss his views on the consultation process."
Among the issues the three men are expected to discuss is the UK Government's consultation on the legality of an independence referendum.
On Friday the Advocate General, Lord Wallace of Tankerness, is due to set out the UK Government's legal position at Glasgow University.
Mr Salmond has claimed he has unsuccessfully sought meetings with Mr Cameron on six occasions in the past.
A spokesman for Mr Salmond said tonight: "This is a very welcome development, and represents real progress - it is much better than the initial reaction last Friday to the First Minister's request for a meeting with the Prime Minister and Deputy Prime Minister.
"We look forward to these meetings being arranged soon, and we will have them in any order the UK Government wish.
"The First Minister is of course very happy to meet with the Scottish Secretary, as he always is."
He said the meetings would have to be after he has updated the Scottish Parliament next Wednesday on the SNP's consultation on referendum arrangements.
"Thereafter, meetings can take place hopefully very soon," the spokesman added.
"We believe it is to everyone's benefit that these meetings are informed by the published consultation documents of both the UK and Scottish governments, so that Mr Moore, Mr Cameron and Mr Clegg can see what our proposals are - and we look forward to the meetings taking place."
Mr Moore said he wanted to meet the First Minister on Thursday to "start making progress" on resolving the differences between the two governments.
He said: "Since Tuesday, when I set out our plans for how Scotland can hold a legal referendum, I have spoken to the First Minister and asked him to meet for talks. I have also written to him.
"We want this referendum made in Scotland and we should start the work this week in the nation's capital.
"There are real legal problems that need solved and I hope we all share the desire to have a legal, fair and decisive referendum."
The UK Government has offered to give the Scottish Parliament temporary power to hold a legally secure referendum, provided it is a simple yes or no vote on full independence.
Mr Salmond, who wants a second option of 'devo max' on the ballot paper, has accused Westminster of interference and "bullying", insisting his party has a democratic mandate to hold a referendum on its own terms.
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