The Sinn Féin president believes the way "has been cleared" for agreement next week at talks in Scotland on the restoration of powersharing with all outstanding issues resolved.
Speaking after a meeting with Tony Blair at the prime minister's residence at Chequers in Buckinghamshire, Gerry Adams insisted that concerns such as republican backing for policing and resolution of the paramilitary fugitives or on-the-runs issues was possible.
"The focus of our discussions today was the restoration of the political institutions. Mr Blair told us that it is his firm resolve to see working institutions in place by November 24th," Mr Adams said.
"There is no more important work in the time ahead for the two governments and the parties than reaching agreement. Sinn Féin believes that a deal is possible on all of the issues. It will become clear whether or not the DUP are up for an agreement. If they are, the opportunity is there - the way has been cleared."
The DUP has insisted that Sinn Féin support for the PSNI is a prerequisite and the party is strongly opposed to any amnesty for on-the-run para- militants. The issue could be a deal breaker, sources have said.
Despite his insistence that his party had honoured all commitments and his overall positive tone, Mr Adams dismissed suggestions of a contingency deal on powersharing which would not have to be implemented until after the November deadline imposed by the Irish and British governments.
He explicitly rejected a conditional agreement which would conclude next year after a series of agreed steps involving the governments and the DUP.
London sources had been referring to such an arrangement. However, this has been countered by officials in Dublin.
Downing Street has now also dismissed reports that Mr Blair and Taoiseach Bertie Ahern were considering a deal permitting the parties to delay fulfilling any obligations beyond the November deadline.
Mr Adams said the focus should now be on the next step by DUP leader Ian Paisley.
"I am not going to second-guess what Ian Paisley is going to do," he said.
"The only one who can speak for Ian Paisley is Ian Paisley. While [ the DUP] can refuse to come on board, the most they can do is delay devolved government."
Mr Adams said he understood the DUP's position.
"I do not underestimate the challenge the DUP is facing over the next week. It is a big challenge. However, republicans have honoured every commitment that they have made. We should all be about serving the people and we can best do that by being part of an administration."
Mr Adams meets Mr Ahern on Monday before they depart for St Andrews.
The Northern Secretary, Peter Hain, has already written to the party leaders outlining draft legislation on changes to the Stormont institutions and on plans to devolve policing and justice powers.
These draft legislative clauses will form the basis of next week's talks in Scotland. Mr Adams said his party was studying the clauses and would not comment further on them, although SDLP leader Mark Durkan has again criticised any plans to bar Ulster Unionists or members of his party from Executive positions if they do not support the election of DUP and Sinn Féin nominees to the position of first and deputy first minister.
The leaders of the four main churches yesterday issued their appeal for progress to be made at the talks in Scotland.
The Church of Ireland and the Catholic archbishops of Armagh, the Presbyterian moderator and the Methodist president strongly encouraged both governments and the Northern parties to concentrate on progress.