Dublin officials were also upbeat about the peace process.
Minister for Justice Michael McDowell, who with Taoiseach Bertie Ahern and Minister for Foreign Affairs Dermot Ahern, met the Sinn Fein delegation, said he had no evidence to suggest the IRA had been involved in criminal or other activity since its announcement in July.
"If you ask me do I see disturbing signs that they are being two-faced on this issue, I don't," Mr McDowell said.
Mr Dermot Ahern said if the IRA did deliver on decommissioning, he believed the DUP would share power with Sinn Fein.
"How long that will take I don't know, but I do believe we are on the cusp of something major in our society, not only just in Northern Ireland but on the island of Ireland, if a momentous decision is made by the IRA in effect to go out of business," he said.
Describing yesterday's meeting which lasted nearly two hours as "positive", Mr Adams said Sinn Fein was seeking commitments from the Government and Britain to move the process forward once decommissioning took place.
"The rest of us who have political responsibilities, particularly those in government, need to be prepared when that happens to be able to move forward to exploit in the national interest and in the advancement of the peace process, the huge opportunity that is going to open up," he said.
Mr Adams also acknowledged that the issue of policing - Sinn Fein's continued refusal to co-operate with policing boards - would have to be addressed. There were a number of outstanding issues, most of which were "mechanical", he said.
"There are some outstanding issues, and I made a case of asking the Government to help us in getting those issues resolved."
Mr Adams also said the DUP and Ian Paisley should be given "the benefit of the doubt" in relation to how that party might react to IRA decommissioning.
"Let him be given the bit of space to come to all of this in a timely and a positive way," he said.
During the meeting, Sinn Fein TD Caoimhghin O Caolain also raised the issue of republican prisoners, including the killers of Det Garda Jerry McCabe, and according to Mr McDowell suggested all might be released as a goodwill gesture.
Mr McDowell said the Government ruled this out completely.