Peter Kilfoyle, a former Labour defense minister, is to table questions after repeated allegations that Mr Bush made the threat at a meeting with Mr Blair in the White House in April 2004. He said yesterday he would also ask Mr Blair what he knew of US plans to attack the Iraqi town of Falluja at that time.

Mr Kilfoyle said he would also ask Mr Blair about what Mr Bush wanted UK troops to do in Iraq outside the area of initial deployment, in the south-east of Iraq. It is known that al-Jazeera was criticized by the Bush administration and US generals in Iraq because of its coverage of American military tactics and captured US soldiers. It is understood the US military had already threatened to close down the al-Jazeera bureau in Baghdad.

It was reported at the time that the US general Mark Kimmet had demanded the removal from Falluja of al-Jazeera.

It has also been widely reported that an American request for British troops to help support the Falluja operation was on the agenda of the White House meeting. Soldiers from the Black Watch regiment were subsequently deployed to help the US south of Baghdad.

British commanders were urging Mr Blair to send extra forces to Iraq but they insisted they should be deployed only on British terms. Privately they were critical of US military tactics though British officials said at the time that Mr Blair was not prepared to criticize US forces.

Mr Kilfoyle has said there are unanswered questions about the talks between Mr Blair and Mr Bush on the attack on Falluja and what he calls “the subsequent deaths of many hundreds of civilians”. A Foreign Office memo entitled Iraq: The Medium Term, dated May 19 2004 and leaked to the Sunday Times, referred to “heavy-handed” US tactics that had “fueled” opposition and “lost us much public support inside Iraq”.

It said the treatment of detainees at Abu Ghraib [jail] “sapped the moral authority of the coalition” and Britain was struggling to get the US to adopt the more tactful approach it wanted.