Boris Johnson has been urged to appear before a panel of senior MPs shortly after Parliament returns next month.
The prime minister is yet to be grilled by the Commons Liaison Committee – made up of select committee chairs – since taking office in July.
The committee’s new chairman Sir Bernard Jenkin has written to the PM to schedule a two-hour slot “well before the end of June”.
Mr Johnson is yet to respond to the request.
In his letter, Sir Bernard said the committee would allow MPs to subject the prime minister to “more detailed scrutiny” than is possible in the Commons chamber.
“At this difficult time, it is of crucial importance that Parliament is able to hold government to account,” added the Tory MP for Harwich and North Essex.
Sir Bernard was appointed to his new role on Wednesday, despite a cross-party attempt to block it after a dispute over the procedure.
He had been nominated to chair the committee by the government, even though he no longer chairs a committee of his own.
The committee, which has held scrutiny sessions with prime ministers since 2002, normally puts forward a chair from among its own members.
Sir Bernard previously chaired the Public Administration Committee throughout the Conservative-Liberal Democrat coalition and up to the last election.
Mr Johnson has previously been accused of dodging scrutiny after pulling out of an appearance at the Liaison Committee last October.
At the time, Mr Johnson justified the decision by saying he had to “focus on delivering Brexit”.
The committee was subsequently disbanded when Parliament was dissolved for December’s election and met for the first time on Thursday since reforming.