The SDLP leader has refused to rule out his party rejecting its two ministerial posts in favour of going into opposition in a restored Northern Ireland Executive.
Mark Durkan warned the governments the change was "unacceptable"
Mark Durkan said the idea arose following a government proposal to change the means of electing first and deputy first ministers at Stormont.
Currently, the top two posts are elected by a majority of unionists and nationalists.
However, during recent talks at Leeds Castle in Kent the British Government suggested all ministers should be selected on the basis of party strength and then endorsed collectively.
But Mr Durkan told the BBC's Politics Show on Sunday that the rule change was to avoid the DUP having to vote for Sinn Fein's Martin McGuinness as deputy first minister.
He said he had warned Tony Blair and his Irish counterpart Bertie Ahern during last month's talks that the change in rules was "unacceptable".
"I did threaten the governments that if that was the outcome of Leeds Castle, the DUP would have a bigger nightmare coming because we wouldn't be nominating ministers, I thought the Ulster Unionists wouldn't nominate ministers and then the DUP would have to put their hands up for a DUP/Sinn Fein coalition.
"That point, that reality check, was one of the things that stopped a bad deal coming out of Leeds Castle."
The Stormont Executive has been suspended for two years
The political institutions in Northern Ireland have been suspended since October 2002 amid allegations of IRA intelligence gathering at the Northern Ireland Office.
On Sunday, the SDLP revealed its proposals for making progress in the political negotiations aimed at restoring the devolved institutions.
The SDLP said its document made clear what "damage" would be done if the DUP were to get the concessions and changes to the Agreement which they are seeking.
In a statement, Mr Durkan added: "Peter Robinson claims that the DUP's proposals are consistent with the fundamentals of the Good Friday Agreement. But that depends completely on what you define the Agreement's fundamentals to be.
"The reality is that without the real fundamentals enshrined in the Agreement - and many others - the SDLP would never have signed up to the Agreement. There would not have been an Agreement."
He said the DUP had not yet responded to his party's proposals for improving accountability, efficiency and collectivity consistent with the Agreement.
Mr Blair and Mr Ahern claimed at the conclusion of the Leeds Castle talks last month that the thorny issues of IRA disarmament and future paramilitary activity appeared to be resolved.
However, the two governments were unable to get the Northern Ireland Assembly parties to sign up to a deal over power-sharing after unionists and nationalists clashed over future devolved institutions.
On Saturday, the Progressive Unionist Party leader said he believed there would be "serious movement" from the IRA in the next few months.
David Ervine told his party's annual conference that devolution would be restored by next February but warned the government that loyalist communities would need help to build on "ground-breaking" IRA moves.