A statement issued in Dublin said the IRA welcomed the moves and had been informed of the broad principles which Mr Adams and Mr Hume would be forwarding to the British and Irish governments.
The IRA said: 'We, our volunteers and our supporters have a vested interest in seeking a just and lasting peace.'
The statement will increase hopes that the IRA and Sinn Fein are serious about pursuing the Hume-Adams initiative.
However, the IRA's endorsement may make both London and Dublin more nervous about reacting to the report which Mr Hume will make to Irish ministers in Dublin later this week.
The IRA bombing campaign continued last night with an attack that caused extensive damage to a hotel in Newtownabbey on the outskirts of Belfast. There were no reports of injuries.
A man wearing a dark blue or black duffle coat with four horizontal yellow bands across the front is being sought by police in connection with a series of IRA bombs that exploded in north London on Saturday. The man was seen in the area before the explosions, with his hood pulled up to cover his face. Four men and a woman were injured by two bombs in west Hampstead; a third exploded outside Finchley Road tube station and a fourth was detonated by anti-terrorist officers.