Peter Hain has hailed last week's talks in St Andrews as an "astonishing breakthrough" in the process of restoring devolved power to Northern Ireland.
The Northern Ireland secretary said he was confident that Sinn Fein and the Democratic Unionist Party (DUP) would soon form part of a power-sharing executive in the province.
Local politicians have until November 10th to respond to a timetable put by the British and Irish governments. If they agree, the Stormont assembly will nominate a first and deputy first minister on November 24th and the process of restoring power will begin.
If a consensus is achieved then the Northern Ireland assembly, which was suspended in October 2002 following allegations of a republican spy ring at Stormont, could be re-established by March 26th.
"It is an astonishing breakthrough," Mr Hain told BBC Radio Five Live, adding: "That is an extraordinary thing that nobody expected to happen within a month or so."
His comments were reflected by DUP deputy leader Peter Robinson, who yesterday described the St Andrews agreement as "immeasurably better" than the 1998 Good Friday agreement, which the DUP refused to take part in.
"The Belfast [Good Friday] agreement allowed those who continued terrorist activity and criminality into government. The DUP have forced republicans, kicking and screaming, down the road of ending paramilitary and criminal activity," he said.
And on Saturday, Sinn Fein leader Gerry Adams told an audience in Belfast: "It is a big concession by republicans to share power with the DUP."
But he said: "Our endeavour is to make peace with [Mr Paisley] and those he represents because we are avowedly anti-sectarian. We are prepared to make peace. Our watchword is equality. Equality includes those citizens represented by the DUP."
Speaking yesterday, Mr Hain said that while there was still work to be done, Northern Ireland politicians' minds had been "concentrated" on the November 24th deadline for agreement to be reached set by the British and Irish governments earlier this year.