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Minister Kwasi Kwarteng says a threat to block school funding in an MP's constituency if he did not vote with the government would be investigated.
The Tory-turned-Labour MP Christian Wakeford made the claim amid wider concerns about the tactics the government uses to pressure MPs.
A group of MPs have met to discuss going public with their own complaints.
The Times reports they are planning to release a secret recording of the government chief whip talking to an MP.
The group, known as the "pork pie plotters", have been meeting regularly to discuss how to oust Boris Johnson, over revelations he attended a drinks a party during lockdown.
In addition to the secret recording of a "heated" conversation with the chief whip, they are also reported to have text messages supporting their claims of intimidation.
The prime minister has been under pressure since he admitted attending a drinks event during the first lockdown, although he says he believed it was a work event.
Mr Johnson has faced calls from some of his own MPs to step down, however he appears to have temporarily survived the challenge to his leadership, with many Conservatives saying they will wait for Sue Gray's report before making a judgement.
The senior civil servant is investigating gatherings that took place on government premises while coronavirus restrictions were in place.
Asked about Mr Johnson's future, Foreign Secretary Liz Truss - who has been touted as a leadership contender - said she supported him "100%" and that she wanted him to "continue as long as possible in his job".
Government whips - the MPs in charge of party discipline - have been trying to shore up support for the prime minister.
But, their efforts triggered discontent among some of those MPs who had been considering calling for a no-confidence vote in Mr Johnson.
On Thursday a group met to compare their dealings with the whips and to consider making the details public.
It came after Conservative MP William Wragg - a critic of the prime minister - accused government whips of threatening MPs with the removal of government investment in their constituencies.
He also said he had received reports of ministers, advisers and staff at No 10 "encouraging the publication of stories in the press seeking to embarrass" MPs.
He said this "would seem to constitute blackmail" and advised colleagues to contact the police.
The BBC has also been told an MP had been threatened with losing their seats under changes to constituency boundaries.
Later, Mr Wakeford, who defected to Labour on Wednesday, said he had been told his constituency would not get a new school if he did not support the government on a vote.
Speaking to BBC North West Tonight, he said: "This is a town that's not had a high school for the best part of 10 years and how would you feel with holding back the regeneration of a town for a vote?"
Asked about the allegation, Mr Kwarteng said it would be investigated but added he didn't "think it's true" and he has "never heard of anything like this" since becoming an MP.
However he said added that if it did happen then it would be "very seriously regarded" and that it isn't "how parliamentary democracy should be conducted".
Asked about Mr Wakeford's complaint on Thursday, Boris Johnson said he had "seen no evidence" to support the allegation.