The row erupted amid fears that the IRA may detonate more "spectaculars" in Britain before renewing the ceasefire and joining the talks process.
The Irish Foreign Minister, Dick Spring, publicly backed the electoral option proposed by John Hume's Social Democratic and Labour Party, with just one constituency for Northern Ireland. That is opposed by the Ulster Unionists, led by David Trimble, who want an election based around existing parliamentary constituencies. Mr Spring also found himself at odds with the British Labour Party when he dismissed proposals for a "hybrid" system, with some representatives elected from a party list and some from constituencies.
Marjorie Mowlam, Labour's Northern Ireland spokeswoman, also issued a veiled warning to ministers about the limits of the Opposition's bi-partisan policy on the peace process.
On Tuesday a Cabinet sub-committee is expected to decide which of the electoral systems to back. Ministers are said to be leaning towards the Unionists' favoured model, which would require less complicated legislation to set up. Elections will almost certainly be accompanied by a referendum north and south of the border.
Mr Spring said: "Whatever system you go for should have broad cross- party support. Some parties favour the single constituency list system. That seems to be getting cross community support from both the DUP [Democratic Unionist Party, led by Ian Paisley] and the SDLP."
Asked about a security clamp-down if the IRA refuses to restore its ceasefire, Mr Spring said: "Internment was a failure in the 1970s. It was a very serious miscalculation. From the point of view of whatever measures are necessary in terms of security if the democratic parties work out an overall settlement, obviously both governments would do whatever was necessary. That's our responsibility."
In an article in the Independent on Sunday, Ms Mowlam says that, on the electoral system, Labour "will support legislation that commands broad acceptance from the parties. A hybrid, with some representatives elected from a `party list', others from constituencies, would be a possible compromise".
She maps out her vision of how the peace process should be pursued, with all parties signing up to the six democratic principles outlined in January's report by former US senator George Mitchell.
Meanwhile David Trimble, leader of the Ulster Unionists, and Ian Paisley, leader of the DUP, warned John Major that they were not prepared to accept a consultation document on the format for the discussions, which are due to begin on 10 June.
Mr Paisley claimed: "It is nothing less than an attempt to muzzle the elected representatives of the Ulster people and find a way of delivering our province into the hands of the Dublin dictatorship."
The path to peace, page 9