The Conservative MP David Davis, backed by the SNP’s Alex Salmond, has said he will present on Thursday the motion accusing the former prime minister of misleading parliament. MPs could debate the issue before the summer if it is accepted by the Commons Speaker, John Bercow.

Sir John Chilcot said in his long-awaited report on the Iraq invasion that the legal basis for the war was reached in a way that was “far from satisfactory”, but he did not explicitly say the war was illegal.

Davis told BBC1’s Andrew Marr Show on Sunday that the motion would say Blair held the house in contempt over the 2003 invasion. He said that if his motion was accepted by Bercow it could be debated before parliament’s summer recess.

Davis said: “It’s a bit like contempt of court, essentially by deceit. If you look just at the debate alone, on five different grounds the house was misled – three in terms of the weapons of mass destruction, one in terms of the UN votes were going, and one in terms of the threat, the risks. He might have done one of those accidentally, but five?”

Salmond said he believed Corbyn’s support would mean the motion had enough cross-party support. “No parliament worth its salt tolerates being misled,” Scotland’s former first minister told ITV’s Peston on Sunday.

He said Blair’s promise to George Bush that he would be “with you, whatever” meant Blair had been “saying one thing to George W Bush in private, and a totally different thing to parliament and people in public”. He said Blair’s actions were “a parliamentary crime, and it’s time for parliament to deliver the verdict”.

The prospect of a contempt vote has opened a rift between Corbyn, the Labour leader, and Angela Eagle, the former shadow business secretary who is challenging him for the leadership.

Asked about the potential vote, Corbyn told Marr he would probably back the motion. “Parliament must hold to account, including Tony Blair, those who took us into this particular war,” he said.

Eagle hinted that she would not support it. Explaining that she had not yet seen the motion, she told the BBC’s Sunday Politics: “We have to make certain that we don’t spend our time in parliament just exacting revenge. I think Tony Blair has been put, rightly, through the mill about the decisions he took. The Chilcot report did that.

“We would be far better learning the lessons and making certain that we don’t fall into the same mistakes if – God forbid – there should be a future situation where these decisions are made.”

John Prescott, who was deputy prime minister at the time of the 2003 invasion, has claimed the Iraq war was illegal.

Writing in the Sunday Mirror, the Labour peer says: “I will live with the decision of going to war and its catastrophic consequences for the rest of my life. In 2004, the UN secretary general, Kofi Annan, said that as regime change was the prime aim of the Iraq war, it was illegal. With great sadness and anger, I now believe him to be right.”

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