Tony Blair is facing a motion of contempt in the House of Commons following the damning verdict of the Chilcot inquiry into the Iraq War.
Jeremy Corbyn said he would "probably" support the motion which accuses the former prime minister of misleading Parliament over the 2003 invasion.
Tory MP David Davis - who accused Blair of "deceit" - will table the motion this week.
Alex Salmond, Scotland's former first minister, told Peston on Sunday that he was backing the motion because a "verdict" on Blair was needed.
“No parliament worth its salt tolerates being misled.”
It comes after Lord Prescott, the deputy prime minister at the time of the 2003 invasion, claimed the Iraq War was illegal.
Davis said if his motion is accepted by Speaker John Bercow, it could be debated before Parliament breaks up for the summer.
He said if the House agreed Mr Blair had held the House in contempt, MPs would have to persuade the authorities "to take the next step".
"I'm going to put down a contempt motion, a motion which says that Tony Blair has held the House in contempt," he told the BBC's Andrew Marr Show.
"It's a bit like contempt of court. Essentially by deceit."
He added: "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?"
Asked if he would back the motion, Corbyn told Andrew Marr: "I haven't seen it yet, but I think I probably would."
Salmond told Robert Peston that Corbyn's backing and the "range of political support" meant that he believed the motion would be backed in the Commons.
He said Blair had said "one thing to George W Bush in private, and a totally different thing to Parliament and people in public."
"That's the Parliamentary crime, the offence, and it's time for Parliament to deliver the verdict," he added.
Tony Blair's former foreign secretary Margaret Beckett, however, said those supporting the contempt motion against Mr Blair were always going to use the Chilcot report "for their own ends".
"It is, however, very clear from the Chilcot report that Tony Blair did not lie, did not falsify intelligence, and that the Cabinet was not misled on the presentation of the legal advice," she said.
"As a member of the Cabinet at the time, I am clear that the Attorney General provided a clear legal basis for military action which was consistent with all the information with which Cabinet had been presented on a regular basis over the previous weeks.”