The DUP will not attend discussions which the NI secretary is expected to hold on the return of devolution.
DUP leader Ian Paisley met the NI secretary
Sources said they had set out a series of time penalties which would apply in response to "any further concessions from the government to republicans".
They claimed devolution would not return for a minimum of two years.
DUP leader Ian Paisley set out an uncompromising position on talks about the return of devolution at a meeting with NI Secretary Peter Hain.
The two men met in London for the first time since the government announced plans to disband the home battalions of the Royal Irish Regiment (RIR).
Mr Hain said the DUP had put its views "extremely strongly and critically," something which he "understood".
Mr Paisley said they told Mr Hain of the "anger" over the RIR decision.
"We told him that the majority of the people of Northern Ireland are very angry," Mr Paisley said.
He said the IRA was "having it their own way" following its statement last Thursday in which it said it was ending its armed campaign and pursuing exclusively peaceful means.
DUP deputy leader Peter Robinson said the "prospects of a return to devolution have been damaged very considerably by the actions of this government".
It is understood the discussions on devolution were set to take place next month.
Mr Hain said there would be "full consultation" on the future of the Royal Irish Regiment home battalions.
"Nobody will take any risks with the security and safety of any individual citizen in Northern Ireland," he said.
Mr Hain said he agreed with the DUP that it was "absolutely essential to get verification that criminality and paramilitary activity will be rooted out of Northern Ireland's politics".
The RIR's NI-based battalions are to be disbanded
"We also agree that decommissioning of IRA weapons is absolutely essential," he added.
Mr Hain said he would like to see the reconstitution earlier than October 2006 of the Policing Board, which holds the PSNI to account.
"My only point is that has to be done by agreement. If we can get agreement, then we can get the DUP representatives on the Policing Board in the numbers that their last election performance suggests that they're entitled to," he said.
Sinn Fein assembly member Alex Maskey urged the DUP to stop "grand standing" and face up to the "new political challenges created by the historic IRA statement".
"There remains no excuse for the two governments in implementing the outstanding aspects of the Good Friday Agreement," he said.
"These are not concessions or bargaining chips. They are basic rights and entitlements designed to create for the first time a level political playing field.
"Even the DUP must now accept that the only situation in which they will have executive power will be in the Good Friday Agreement institutions alongside Sinn Fein."
The SDLP's Alban Maginness said: "The DUP seem to think that they should have a veto on all change - no matter how sensible.
"They expect to be able to hold up the Agreement and undermine what the people of Ireland voted for.
"Now they are learning that they don't have a veto. They need to learn the lessons of this. Instead of getting comfortable with direct rule, they ought to be getting real about restoring devolution."
Following Wednesday's meeting with the DUP, Mr Hain also met relatives of victims of the Shankill bombing.
They wanted to voice their concerns about last week's release of the Shankill bomber, Sean Kelly, a month after he was returned to jail.
The relatives were accompanied by members of the DUP.
Mr Paisley will stay in London for a meeting with Tony Blair on Thursday.
Sinn Fein President Gerry Adams is also expected to meet the prime minister this week.
The Northern Ireland-based battalions of the Royal Irish Regiment are to be disbanded on 1 August 2007, as part of the response to the IRA ending its armed campaign.
The Army will end its support role to the police on the same day.
On Monday, the secretary of state set out a two-year plan on demilitarisation which, he said, would be contingent on the security situation.
Unionists reacted angrily to the move, which nationalists have welcomed.
Mr Hain also announced that troop levels in the province would fall from 10,500 to 5,000 in two years time.