The statement is seen as particularly significant since contacts between the two leaders have played a vital part in creating and maintaining the peace process. It is also important in that Mr Hume has always said the aim should be a complete cessation of violence rather than any temporary ceasefire.
Last night the Taoiseach, Albert Reynolds, said there now existed the best opportunity for peace since partition. He said a decision to end violence completely would be a gigantic step forward. Some reports predict a ceasefire announcement as early as tomorrow, while others are more cautious. But all sides agree that a ceasefire is about to be called.
Two informed sources were yesterday speculating that the IRA would opt for a complete cessation, as stipulated by both the British and Irish governments, rather than the limited or conditional stoppage widely forecast.
One was the Irish tourism minister, Charlie McCreevy, who said in a radio interview: 'I think we are on the verge of a very historic opportunity . . . I would be very hopeful of a complete cessation of violence on the island.'
A similar assessment came from Bill Flynn, a senior business figure who was one of the Irish-American delegation which this week met Sinn Fein leaders in Belfast. Mr Flynn, who some months ago said he believed there would be peace before America's Labor Day (5 September), declared: 'I have learned nothing since I've been here on this visit that would have me change that.'
In their statement, Mr Hume and Mr Adams said that in a new situation the onus would be on the British government to respond positively, both in terms of demilitarisation and in encouraging national reconciliation.
A Northern Ireland Office spokesperson said that if Mr Adams wished to participate in the political process he was already aware of the condition which applied - a firm and permanent renunciation of violence.
Both governments meanwhile are playing down the significance of reports that parts of the 1921 Government of Ireland Act are under discussion in negotiations between London and Dublin. It is reported that the British government is prepared to change the Act's bald declaration of Westminster's authority over Northern Ireland by incorporating a statement that a majority there should decide its future. This is in line with more recent pronouncements on the constitutional position such as the Anglo-Irish agreement and the Downing Street declaration.
Unionist reaction has been mixed, with Ian Paisley's Democratic Unionists taking a harder line than the Ulster Unionists.
The Reverend Roy Magee, a Belfast Presbyterian minister who recently met leaders of Loyalist paramilitary groups, said he believed they wanted an end to violence. But he added: 'It's fair to say that if they felt that something was done to diminish their position within the UK, they would react fairly violently to that.'Reuse content