Written proposals sent to Sinn Fein also spelled out the conditions under which it could join full-scale negotiations by September - putting the issue of weapons decommissioning to one side.
The revelation, whichemerged at the G7 summit in Denver where Tony Blair was discussing Ulster with Bill Clinton, comes just days before a planned Government attempt to revive the peace process.
The Lurgan killings imply that either a faction within the IRA decided to sabotage the process, or that the Republican movement wanted to keep uppressure on the Government.
Loyalist terrorists seeking to avenge the Lurgan murders are believed to have been behind a bomb attack on a car in central Belfast last night.
It was thought the blast was caused by an under-car device and was directed at two senior republicans travelling in it, who were slightly hurt. One was thought to be a member of the Irish Republican Socialist party, the political wing of the terror group the Irish National Liberation Army (INLA).
"This is another appalling terrorism act and it simply underlines the need to move this [Northern Ireland peace] process forward," Mr Blair told reporters as he met Mr Clinton last night. President Clinton expressed his horror at the new violence in Northern Ireland and his continuing support for the British government's approach.
He said the US had been "appalled" at the Lurgan murders and yesterday's act of terrorism. "But I frankly think now the ball is in Sinn Fein's court. We all have to decide. Everybody has decisions to make in life - their decision is are they going to be part of this peace process or not."
British officials insisted that the government was "still committed" to the process, although the Lurgan attack had been a setback. In declining to justify why they believed conditions before the Lurgan killings had "never been better" for Sinn Fein to join the peace talks, they gave the strong impression that the offer reportedly advanced last week in talks with Sinn Fein officials was still open. But at home there were signs that the Conservative leadership might discard the tradition of bilateral support. One source said that Mr Hague "may not feel bound by it".
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