The SDLP leader said Mr Major had told him that the 'door is open' for further talks and Mr Hume said he intended to use it, although they had failed to reach agreement on the detailed plans.
'I would be absolutely delighted if I were able to tell you that the Prime Minister agreed with me totally and was going to act immediately because I think we would have peace within the week in Northern Ireland if that were to happen,' Mr Hume said after the meeting.
'I believe that we have a real opportunity for lasting peace. I am not talking about secret deals because that would not solve our problems,' he said on Channel 4.
Last night there were signs that Mr Major is hoping to reconvene the round- table talks on Ulster's future, if there is a prospect of agreement on the plans agreed between the British and Irish governments for an elected assembly.
He told Mr Hume at their hour-long meeting that the resumption of the talks process was central to the Government's approach. He will hold bilateral meetings next week with Ian Paisley, leader of the Democratic Unionists, and James Molyneaux, leader of the Ulster Unionist Party, before deciding whether to call the party leaders to talks.
Mr Major told the Commons that he hoped to see a resumption of the cross- party talks on the constitutional future of Ulster 'as speedily as possible'. John Smith, the Labour leader, urged Mr
Major not to miss the 'window of
The Prime Minister is keen to carry on the momentum of the calls for an end to violence but there is a growing realisation it could mean a return to the long haul. Ulster Unionist leaders attached importance to remarks by Mr Major on the need for 'a proper constitutional structure for local government', but that would fall far short of their expectations for devolution of power to the province and the Prime Minister's office denied any special significance was intended.
In Belfast and Dublin Mr Hume's mention of the possibility of peace within a week has maintained and even increased the high level of public and political interest in the Hume-Adams initiative. His assessment will increase pressure on the British and Irish governments to take the initiative further.
Last night Dublin showed signs of responding to this pressure when Dick Spring, the Irish Foreign Minister, declared that a recent speech by him should be seen as 'a complement to, rather than a substitution for' Mr Hume's efforts.
Gerry Adams, the Sinn Fein president, said he looked forward to hearing Mr Hume's assessment of Mr Major's response at the Downing Street meeting. He said Mr Major had originally rejected the Hume-Adams initiative, but had been given the opportunity to change his mind.
IRA bombers yesterday tried to kill soldiers and police officers guarding Catholics from loyalist paramilitaries in west Belfast, the RUC said. A 25lb bomb packed with metal nuts and bolts - described by police as a 'particularly evil device' - was found hidden behind a fence close to a roundabout on the Stewartstown Road near the Twinbrook and Poleglass housing estates.Reuse content