Mr Twigg also disputed a news report that said he had "defended" Tony Blair in the Commons last Wednesday, arguing that his comments were meant to find out on behalf of constituents whether the Prime Minister thought Chilcot's findings confirmed or otherwise the main accusations levelled at Mr Blair, namely that he had lied to or misled MPs, that intelligence findings had been distorted or that he had broken worldwide law by going to war.
David Davis said "quite a lot" of MPs already support the motion which will claim Mr Blair deceived MPs over the invasion.
Mr Davis said: "The public want to see something done, there's no doubt about that".
Tony Blair could face a motion of contempt in the House of Commons over the 2003 invasion of Iraq - a motion that Jeremy Corbyn has said he would probably support.
"'No parliament worth its salt tolerates being misled", he said.
Chilcot's report on the Iraq War substantiates claims that the effect of the invasion has given rise to terrorism and unrest that has engulfed the region with no signs of abating.
Mr Davis, the former shadow home secretary, told the BBC's Andrew Marr show: "I'm going to put down a contempt motion, a motion which says that Tony Blair has held the House in contempt".
Blair defended his decision to join the war, insisting it was taken "out of good motives" and that he believed the world was a better place now that former Iraqi dictator Saddam Hussein had been removed.
Strictly speaking, it's any act - or failure to act, that may "prevent or hinder the work of either House of Parliament".
'I haven't seen it yet but I think I probably would [vote for it]'. Weapons of mass destruction (WMD) were the basis of launching the war.
Mr Salmond said that MPs had a duty to respond to the findings.
Tony Blair immediately called a press conference after the report was released, to express sorrow over the outcomes of the war.
The former deputy Prime Minister has said his guilt over the invasion will haunt him forever. In the case of being passed, it could result in Tony Blair's ejection from the Privy council.
However, Dame Margaret Beckett, a close supporter of Mr Blair, said: "The Chilcot report was never going to settle the arguments about the war".
This refers to the editorial "Chilcot report" (July 09). Flawed intelligence, a rush to military action before the diplomatic options had been exhausted, the breakdown of proper Cabinet government, flawed intelligence, poor planning for the post war period, the legality of the war, inadequate military equipment, the list is pretty damning and will be debated for many months.
A spokesperson for the group of MPs organising the censure motion said parallel legal action threatened by families of soldiers who served in the Iraq War could proceed separately to their efforts.