On the second day of a visit to Northern Ireland, Mr Major responded sharply, describing the ceasefire as a self-serving and cynical exercise intended to encourage the gullible.
The Irish government again expressed disappointment with the IRA announcement, indicating that it would not be pressing London to provide the clarification of the Downing Street Declaration demanded by Sinn Fein.
The Taoiseach, Albert Reynolds, was said to regard such a limited ceasefire as a personal snub, and it is clear that any IRA hope of driving a wedge between the two governments looks doomed to failure.
But a much more upbeat assessment came from the head of the Irish Catholic church, Cardinal Cahal Daly. Contradicting Mr Major, Dr Daly said he believed the IRA's ceasefire was a sincere gesture rather than a cynical move.
Pointing out that for two decades the IRA had ruled out temporary ceasefires, Dr Daly added: 'I believe there should be some positive response to this, which in IRA and Sinn Fein terms is a significant development. Admittedly it is only 72 hours, but that is something. This is a gesture; not enough, but it is a gesture. Let's not dismiss it.'
Unionist politicians agreed with Mr Major's assessment. The Ulster Unionist MP David Trimble said: 'This business about clarification is obviously a lure to get the British government into discussions in advance of a cessation, and it is obviously dishonest.'
Loyalist violence continued yesterday, with three men being seriously injured in two shootings. Two Catholic men were shot when a gunman raked their van with gunfire as they arrived for work on a Protestant housing estate.
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