In an attempt to influence the internal republican debate on how to respond to the Downing Street peace declaration, he urged them to make 'one of the greatest acts of moral courage of this century' and give up violence.
In a closely argued five-page statement which he urged republican activists to read, Mr Hume contended that the Downing Street declaration contained a clear British acceptance of the right of the Irish people to self-determination - Sinn Fein's central demand.
He added that another key republican demand, for an organised political alternative to 'armed struggle,' had been met by the Irish government's promise to establish a 'forum for peace and reconciliation'. Dublin has said Sinn Fein would be invited to take part if the IRA ends its violence.
Mr Hume has been a central figure in the peace process, having been the original advocate of the concept of having the British and Irish governments address themselves directly to the stated requirements of the republican movement.
The Hume-Adams agreement, which he formulated with the Sinn Fein president, Gerry Adams, was a forerunner of the Downing Street declaration. Mr Hume's judgement on the declaration, which he said yesterday could be reconciled with Hume-Adams, will, therefore, be studied carefully by Sinn Fein.
The republican response to the declaration is due before the end of this month. It is already apparent, however, that the answer is unlikely to be a definitive and clearcut 'yes or no'.
Sinn Fein and the IRA regard themselves as being in the early stages of a negotiation with the British Government. The IRA has no intention of calling off its campaign in the near future , while Sinn Fein has no intention of bringing the peace process to an early close, one way or the other, before it fully 'teases out' what may be on offer from the Government.
Sinn Fein's interim approach has been to call for clarification of the declaration, and that request was yesterday supported by Mr Hume. He said in an interview: 'Given that the prize is peace, everybody should do everything in their power to ensure it is reached.
'If clarification is needed by any section of our people, the Government have the means to do it and they should do it.'
The Irish government has indicated it expects Mr Hume to provide some clarification to republicans, although he apparently would prefer that to happen directly rather than for him to have to act as an intermediary. The support of Dublin and Mr Hume will increase pressure on London to meet Sinn Fein's request for clarification.
On the Unionist side, meanwhile, James Molyneaux, the Ulster Unionist Party leader, last night argued that the IRA had already refused to accept the declaration, and said the way was now clear for 'a really effective anti-terrorist campaign'. Mr Hume, by contrast, is continuing to press and hope for an IRA cessation, which he envisages as opening the door to a new stage of debate and negotiation including both governments and all the
He said peace was 'an enormous challenge which will require from the republican movement, given the experience its members have been through, one of the greatest acts of moral courage of this century. But at the end of the day it is moral courage that gives real leadership and creates truly historic opportunity.'
Peace would bring an influx of new investment which research had indicated could create, in Ireland as a whole, some 75,000 jobs, he said. 'With peace, the border will, in fact, be gone. The British Army checkpoints are the only remaining signs of a border anywhere in the new Europe. They will disappear with peace and natural social and economic activity will resume for the first time in 70 years.'
Two Irish Army bomb disposal experts were injured yesterday when a device they had apparently made safe blew up at a Dublin army barracks. The device had been sent to Sinn Fein's headquarters in the city.
Earlier yesterday another letter bomb exploded at the Dublin offices of the Sinn Fein newspaper, An Phoblacht.