LONDON — Boris Johnson returned to Britain on Saturday, feeding expectations that he would seek to reclaim his old job after the resignation of Prime Minister Liz Truss last week. His former chancellor of the Exchequer, Rishi Sunak, also seemed poised to join the race to replace Ms. Truss.

Mr. Johnson, who had been vacationing in the Dominican Republic, won the backing of his former home secretary, Priti Patel, a significant endorsement from a prominent figure on the right wing of the Conservative Party.

Allies of Mr. Johnson claimed on Saturday afternoon that he had picked up support from more than 100 lawmakers. That is substantially larger than the number who have publicly declared for him. But if he were to cross that threshold, it would significantly raise the odds of him returning to 10 Downing Street.

Contenders for party leader are required to have nominations from at least 100 of the 357 Conservative lawmakers to advance to a second round of voting, among the members of the party in Britain, a group with whom Mr. Johnson remains popular. Mr. Sunak already has 128 votes from party lawmakers, according to an unofficial count by the BBC.

“Boris Johnson has more than 100 backers,” James Duddridge, a Conservative member of Parliament who is close to him, posted on Twitter, without naming any.

Candidates have until 2 p.m. Monday to gather those nominations. On Monday, the party will hold two rounds of voting to winnow the field to one or two candidates. If two remain, party members will cast ballots later in the week.

Mr. Johnson, who was forced out of office in July after a series of scandals prompted a rebellion of Conservative lawmakers and ministers, trails Mr. Sunak in counts of declared lawmakers compiled by the BBC and other news organizations. The BBC said Mr. Johnson had 53 votes, while Penny Mordaunt, the leader of the House of Commons who has declared her candidacy, had 23.

Other tallies put Mr. Johnson’s numbers higher. Reporters for the BBC and The Times of London, citing people close to him, said he was in a position to be on the ballot next week, if he chose to be. Without publicly declared names of backers, however, it was impossible to determine the credibility of that claim.

Crossing the threshold of 100 votes would make Mr. Johnson the automatic favorite because opinion polls suggest he would beat Mr. Sunak in a contest with party members. For Mr. Sunak, that would be a repeat of his experience this summer, when he won the most votes among lawmakers, only to lose to Ms. Truss among the members.

Much will depend on whether other figures from the right, like Suella Braverman or Kemi Badenoch, decide to run — and if they do not, who picks up their votes.

Mr. Johnson remains popular with the grass roots of the party, which has prompted some Conservative columnists and commentators to try to stop his candidacy from getting out of the starting gate.

Andrew Neil, a prominent broadcaster, wrote in The Daily Mail, “It’s time for the Tories to put the country first and vote for Rishi Sunak, the man the markets trust.” Charles Moore, in The Telegraph, wrote that he could see “Boris storming back in different circumstances.” But he added: “I don’t see it working right now. True Boris fans will have the courage to tell him to sit this one out.”

David Frost, who negotiated the post-Brexit trade deal with the European Union for Mr. Johnson’s government, urged lawmakers to vote for Mr. Sunak. “Boris Johnson will always be a hero for delivering Brexit,” he wrote on Twitter. “But we must move on. It is simply not right to risk repeating the chaos & confusion of the last year.”

Other commentators warned that choosing Mr. Johnson would deepen fears about Britain’s stability that were stirred by Ms. Truss’s tax-cutting plans. The ratings agency Moody’s lowered its economic outlook for Britain to “negative,” citing political instability and high inflation.

Still, Mr. Johnson’s supporters view his candidacy as a chance to rebuild the Conservative Party after the chaos and reversals of Ms. Truss’s six weeks in office. Some are betting on him because they hope that he can save their seats in a general election, given the huge lead that the opposition Labour Party now holds in the polls.

“I’m backing @BorisJohnson to return as our Prime Minister, to bring together a united team to deliver our manifesto and lead Britain to a stronger and more prosperous future,” Ms. Patel tweeted Saturday afternoon.