William Wragg, chairman of the Commons Public Administration and Constitutional Affairs Committee, said he has received reports of conduct amounting to "blackmail".
It came as it was reported senior civil servant Sue Gray had found the email from a senior official to Prime Minister’s principle private secretary Martin Reynolds warning him the May 20, 2020 party should not go ahead.
The email is believed to have been copied to an official in Mr Reynolds’s office and to Mr Johnson’s former senior aide Dominic Cummings, who has accused Mr Johnson of lying over his accounts given around the Downing Street garden party.
Speaking on Thursday, Mr Wragg gave a statement on the alleged “intimidation” and “blackmail” some MPs had faced.
He said: “In recent days, a number of Members of Parliament have faced pressures and intimidation from members of the Government because of their declared or assumed desire for a vote of confidence in the party leadership of the Prime Minister.
“It is, of course, the duty of the Government whip’s office to secure the Government’s business in the House of Commons.
“However, it is not their function to breach the ministerial code in threatening to withdraw investments for Members of Parliaments’ constituencies which are funded from the public purse.
“The intimidation of a Member of Parliament is a serious matter, reports of which I am aware would seem to constitute blackmail.
"As such it would be my general advice to colleagues to report these matters to the Speaker of the House of Commons and the Commissioner of Metropolitan Police."
Mr Wragg is one of several of Tory MPs to publicly admit to submitting a letter to the chairman of the backbench 1922 Committee Sir Graham Brady calling for a no-confidence vote.
Speaking as the committee prepared to take evidence from Cabinet Office minister Stephen Barclay, Mr Wragg said the conduct of the Government whips’ office threatening to withdraw public funding from MPs' constituencies may have breached the ministerial code.
His claims were backed up Christian Wakeford, the MP who defected from the Tories to Labour over ‘partygate’. Mr Wakeford said he was threatened he would not get a high school in his constituency if he did not vote in a certain way.
Speaking to BBC North West, he said: “I was threatened that I would not get the school for Radcliffe if I did not vote in one particular way. This is a town that’s not had a high school for the best part of ten years.
“How would you feel when holding back regeneration of a town for a vote. It didn’t sit comfortably. That was really starting to question my place where I was and ultimately to where I am now.”
Speaking on a visit to Taunton, Mr Johnson claimed he was not aware of any threats.
He said: “I’ve seen no evidence to support any of those allegations.
“What I am focused on is what we’re doing to deal with the number one priority of the British people, which is coming through Covid."
Asked during a visit to a diagnostics centre if he would look for evidence to support the allegations, the Prime Minister said: “Of course.”
Labour's Deputy Leader Angela Rayner MP claimed the country “deserved better”.
She said: “These are grave and shocking accusations of bullying, blackmail and misuse of public money and must be investigated thoroughly.
"The idea that areas of our country will be starved of funding because their MPs don't fall into line to prop up this failing Prime Minister is disgusting.
“On the day Labour is setting out plans to deal with the cost-of-living crisis affecting the whole country, the Tory party continues to descend further into chaos of its own making.”
Liberal Democrat MP Alistair Carmichael labelled Mr Wragg’s statement “explosive”.
He said: “We may all have been somewhat dulled to the constant stream of sleaze allegations surrounding this Government, but the suggestion that funding – from the public purse – is being tampered with to protect the Prime Minister is beyond outrageous.
"The Treasury is not supposed to be Boris Johnson’s slush fund, used to reward cronies and punish the principled.
“The only way to stop this sort of behaviour is for MPs to call it out. It is unacceptable and probably illegal.”
The SNP's Westminster deputy leader Kirsten Oswald urged Tory MPs to remove Mr Johnson from office.
She said: "These reports from a senior Tory MP of intimidation, blackmail and threats, including withholding public money from constituencies, towards Tory backbenchers who may have backed calls for a confidence vote in the rule-breaking Prime Minister are serious, dangerous and must be investigated.
"Boris Johnson is meant to be tackling the challenges facing the UK, including the cost-of-living crisis hammering households. Instead he is running a bungled mafia-style operation from Downing St.”
Speaker Sir Lindsay Hoyle said it would be a “contempt” to obstruct MPs in doing their duties by trying to “intimidate” them.
He told MPs: “Those who work for them are not above the criminal law. The investigation of allegedly criminal conduct is a matter for the police and decisions about prosecution are for the CPS. It will be wrong of me to interfere with such matters.
“While the whipping system is long-established, it is of course a contempt to obstruct members in the discharge of their duty or to attempt to intimidate a member in their parliamentary conduct by threats.”
A Downing Street spokesman said: “We are not aware of any evidence to support what are clearly serious allegations.
“If there is any evidence to support these claims, we would look at it very carefully.”