The meeting took happened, but neither side divulged what was discussed.
Mr. Johnson is in the second position, with 53 supporters.
However, his campaign asserts that he has the support of 100 members of Congress, the minimum number required to officially enter the race.
Mr. Sunak’s followers raised questions and demanded proof from the former prime minister.
The voting intentions of only 204 out of 357 Conservative MPs, leaving more to declare their interest.
If this is not the case, the Conservative party members will vote online, and the results will be released on Friday.
On Saturday, members of Congress openly declared their support for their preferred candidate.
Mr. Sunak received support from all factions of his party, including the right, as well as people such as Mr. Johnson’s former chief of staff Steve Barclay, his former Brexit minister Lord Frost, Kemi Badenoch, and Northern Ireland minister Steve Baker.
Mr. Baker, a key MP from the party’s right-wing, stated that Mr. Johnson would be a “certain disaster” and expressed particular concern on an ongoing parliamentary investigation into whether the former prime minister lied to Parliament about Covid rule-breaking.
He told Sky News that a significant number of Conservative MPs would “refuse to sacrifice their integrity” to back Mr. Johnson on this subject.
Ms. Badenoch, who made a significant effect in the previous Tory leadership contest but has ruled herself out this time, stated in the Sunday Times that Mr. Sunak was “the serious, honest leader we require.”
Mr. Sunak has the support of former chancellor and health secretary Sajid Javid, Security Minister Tom Tugendhat, and former deputy prime minister Dominic Raab, despite not having officially declared his candidacy.
Mr. Raab told the BBC, referencing the parliamentary investigation confronting Mr. Johnson, “We cannot move in reverse. We cannot endure another Groundhog Day or episode of the Partygate soap opera “.
He expressed high confidence that Mr. Sunak will run, adding: “I believe the economy will be the deciding factor in this scenario. I believe that Rishi’s summer strategy is still the correct plan now.”
An associate of former home secretary Suella Braverman told the PA news agency that she had been “heavily courted” by both Mr. Johnson and Mr. Sunak and would likely decide on Sunday which candidate she would support.
Former commerce secretary Andrea Leadsom stated that Ms. Mordaunt was the unifying choice; an experienced minister and “vigorous Brexiteer.”
In an editorial published in the Express on Sunday, Ms. Mordaunt outlined her strategy to “unite the party and the country” and stated that the Conservatives had “allowed ourselves to become distracted by internal disagreements.”
She emphasized the need to “make Brexit work,” “concentrate on the potential of every citizen,” and “protect our Union and territorial integrity.”
Bob Seely, a member of the Conservative Party, stated, “I believe we have a common responsibility to apologize to the country” and added that he believes Ms. Mordaunt has the best opportunity of offering “unity and leadership” within the party.
Mr. Johnson’s possible quest to return to power comes barely seven weeks after his departure from No. 10 Downing Street.
She announced her resignation on Thursday following a series of embarrassing U-turns necessitated by bad market reaction to her tax policy.