Republicans must demonstrate a commitment to ending paramilitarism for good, David Trimble has said.
Mr Trimble was speaking at his party's annual conference
However, the Ulster Unionist leader conceded that political progress in Northern Ireland could proceed without IRA decommissioning being completed immediately.
He told his party conference that what was needed was a sense that paramilitarism was coming to an end soon.
Decommissioning of weapons, an end to paramilitary violence and the winding up of paramilitary organisations had to take place, he insisted.
However, every "jot and tittle" did not need to be completed before proceeding with re-establishing the institutions, he said.
Mr Trimble told the conference in Armagh there could be no excuses for paramilitary violence such as "internal house-keeping" and that foot dragging on decommissioning and on commitments to peace and democracy could not be tolerated.
"Neither the government's formula nor ours say that everything must be done first. Rather both envisage a sense that paramilitarism is coming to an end soon," he told delegates.
"And perhaps the most important aspect of that sense is an acknowledgement by republicans that the Belfast Agreement is a settlement - that it provides the full and final closure of the conflict."
He added: "The issue is simple. Republicans know what has to be done - it has been absolutely clear since April. They need to make up their mind. Society cannot be expected to wait for ever."
Mr Trimble said republicans may regard these as huge steps, but they were not simply unionist demands.
"This is what the Agreement sets out again and again as its overriding objective," he told party members.
The UUP leader also posed a question to dissident MPs Jeffrey Donaldson, David Burnside and Martin Smyth, who faced disciplinary action after their decision in June to refuse to adopt the party line at Westminster.
Mr Trimble asked: "Gentlemen, would you please decide whether you prefer to be independent members or if you really do want to be part of a political party?"
Mr Trimble posed question to the three MPs
However, Mr Donaldson said Mr Trimble was "misrepresenting" his position.
Earlier, Mr Trimble said policing and justice powers could be transferred to a new power-sharing executive within two years.
The transfer of policing and justice is one of the most sensitive elements of the current negotiations aimed at restoring devolution to Northern Ireland.
Speaking on BBC's Inside Politics programme, Mr Trimble said it was impossible to predict a precise timescale as the move depended on the creation of the right context.
Sinn Fein's Mitchel McLaughlin welcomed Mr Trimble's speech for its backing of the Good Friday Agreement.
He said the war on the streets had ended and it was time to deal with the legacy of that conflict in a measured way as quickly as possible.
'As never before'
PUP leader David Ervine said he believed Mr Trimble and Sinn Fein President Gerry Adams were close to a deal.
"Gerry Adams is going to be responsible for something that
changes this process forever," he told his party's annual conference in east Belfast.
"He is going to take the IRA where they have never been before. The question is will David Trimble respond as never before."
After meeting Taoiseach Bertie Ahern in Dublin on Saturday, SDLP leader Mark Durkan said some people may be suspicious that a deal was being put together before an election campaign.
Democratic Unionist Party deputy leader Peter Robinson said: "An assembly election cannot come soon enough to allow unionists to rid themselves of the old, tired and out-of-ideas Ulster Unionist party."
The devolved administration was suspended a year ago amid allegations of IRA intelligence-gathering in the Stormont government.
Assembly elections were postponed in May but there is speculation over an autumn poll.
Behind-the-scenes negotiations aimed at brokering a deal which could lead to the restoration of devolution are understood to be continuing.
During the past few weeks, Mr Adams and Mr Trimble have held a series of meetings aimed at breaking the political impasse.
The pro-Agreement parties and Mr Blair have said that they want the election to be held in a positive atmosphere.