A powerful Commons committee should investigate whether Keir Starmer misled parliament over the appointment of Peter Mandelson as ambassador to Washington, Ed Davey has said.

The Liberal Democrat leader called for the prime minister to be investigated by the privileges committee to determine whether he committed contempt of parliament, an offence that can lead to a ministerial resignation.

The prime minister is under mounting pressure to explain what he knew about the pre-appointment process, after the Guardian revealed security officials recommended the former Labour peer be denied security clearance, but were overruled.

On Thursday night, Starmer sacked Olly Robbins, the most senior civil servant at the Foreign Office. On Friday morning, Darren Jones, the prime minister’s chief secretary, described the controversy as a “failing of the state”.

Davey said on Friday: “We need to get to the bottom of exactly what Keir Starmer knew when, and whether he intentionally misled parliament over this appalling scandal. The public deserves the truth, not another cover-up.

“If it turns out that Starmer was aware at the time that Mandelson’s security vetting was overruled, that would represent a major abuse of power and a betrayal of the national interest.

“Boris Johnson eventually resigned after misleading parliament. If Starmer has done the same, he must be held to the same standard.”

The Lib Dems will push for the Commons to debate a motion on Monday to open a privileges committee inquiry. Johnson resigned as an MP in 2023 after that committee found he had deliberately misled parliament.

Downing Street says the prime minister did not know until this week that Mandelson had failed his security vetting. Starmer will appear before parliament on Monday to explain his version of events.

Jones told Sky News on Friday: “The prime minister is as furious as everybody else, because he would expect … to have been told that UK security vetting did not recommend Peter Mandelson to be appointed.

“He’s furious with the state. I mean, this is a failing of the state. It is a security failing.”

Jones added that he had suspended the power of civil servants to override the recommendations of vetting officials, telling the BBC he had been “astonished” to discover on Thursday that they had that power in the first place.

Kemi Badenoch, the Conservative leader, said on Friday she did not believe the prime minister’s denials.

“It is completely preposterous that for us to believe that civil servants would have cleared a political appointee who had failed security vetting,” she told BBC Radio 4’s Today programme.

“We would not have found out for this, if not for the Guardian. So I’m afraid the story does not stack up. The prime minister is taking us for fools.”

Badenoch joined other opposition MPs in calling for Starmer to resign immediately.

Siân Berry, the Green party MP, said: “Keir Starmer has lied and lied again over his decision to appoint Peter Mandelson and he must resign. Starmer told parliament ‘due process’ had been followed. This report makes clear that was untrue.”

Nigel Farage, the Reform UK leader, posted on X: “Keir Starmer said in February that the security services had given Mandelson ‘clearance for the role’. Now we discover that he has blatantly lied, the prime minister should resign.”

The Labour chair of the foreign affairs select committee, Emily Thornberry, said before Robbins was sacked that her committee would summon him over his previous evidence to ascertain whether he misled MPs.

“My committee asked several times whether red flags had been raised by Peter Mandelson’s vetting process. It seems there were,” she said. “Who overrode these concerns? Why were we kept in the dark? People need to stop messing us about and tell us the truth.”

Jones insisted on Friday the prime minister did not know about the vetting decision. “The prime minister was only made aware of that on Tuesday evening this week, when the documents became available to the Cabinet Office,” he told the BBC.

Downing Street said that Starmer was informed of the vetting override on Tuesday night and ordered an investigation. But the prime minister has also faced questions about why he did not set out the development to MPs as early as Wednesday.

Many Labour MPs privately warned that Starmer’s future would hang on what further evidence emerged of whether the Foreign Office took the decision unilaterally.

“[It’s] hard to see how this isn’t terminal if the PM knew,” one backbencher said.

Another said: “No 10 is telling everyone they didn’t know. This is not credible and no one will believe them unless they produce receipts and sack Olly Robbins.”

A third said the idea that Starmer was unaware “stretches beyond credulity”.