Downing Street was not ruling out fresh talks on Friday with the Northern Ireland parties and the Irish Prime Minister, Bertie Ahern.
No 10 said the process was "just edging forward" after Mr Blair held bilateral talks with Mr Adams and Mr Trimble. "We are determined to crack this. The Prime Minister and the parties are discussing different possible routes through the current impasse but there is no quick fix or instant solution. If there was we would have used it," said a spokesman for Mr Blair.
Mr Adams entered No 10 yesterday, warning that the process was "in tatters". He was more conciliatory later, saying Mr Blair was focused on the issues and that they had "frank" talks about the options.
The Independent has learnt that Mr Adams has assured Mr Blair privately that the IRA ceasefire will hold, but he has been unable to give any guarantees about the surrender of weapons, which Mr Trimble is seeking before allowing the power-sharing executive to be set up.
Mr Trimble is insisting decommissioning needs to start before he can gain the support of Unionists to appoint the executive.
Mr Trimble emerged from talks yesterday with Mr Blair, complaining that Sinn Fein's announcement at the weekend of its two proposed ministers in the Assembly, including Martin McGuinness, Sinn Fein's chief negotiator, had made it more difficult to reach a compromise.
"I'm afraid that following the Sinn Fein conference at the weekend things do not seem to be particularly encouraging.
"The most optimistic thing we can do at the moment is keep pressing away and hope that in time the republican movement will start to implement its part," Trimble said.
Mr Adams stressed he was not putting a deadline on the talks but said the European election campaign would be starting next week, with the Democratic Unionist Party leader, Ian Paisley, threatening to turn it into a referendum against the Good Friday Agreement; and the marching season would begin in five weeks.
n Members of the Northern Ireland Law Society voted last night in favour of independent inquiries into the 1989 loyalist murder of Pat Finucane and into the murder earlier this year of the human rights lawyer Rosemary Nelson.