British Conservative politician Rishi Sunak late Friday reached the minimum threshold to run for party leader, as former prime minister Boris Johnson targeted an audacious comeback.

Cabinet member Penny Mordaunt became the first to formally declare her candidacy, after the UK's ruling party was forced into a second leadership contest following the dramatic resignation of Prime Minister Liz Truss.

"Honoured to be the 100th Tory MP to support #Ready4Rishi," senior backbencher Tobias Ellwood tweeted, as other backers of Sunak also said he had crossed the barrier.

Sunak will automatically become party leader and prime minister if his opponents fail also to win 100 nominations from their fellow Tory MPs.

Security minister Tom Tugendhat, who ran for leader himself after Johnson was toppled in July, issued a thinly veiled appeal to the scandal-tainted ex-leader to stay out of the race.

"This is no time for political games, for settling scores, or for looking backwards," Tugendhat said as he also endorsed Sunak late Friday.

Neither Sunak nor Johnson has publicly declared they are running.

But Johnson cut short a Caribbean holiday to take part in the accelerated contest, which will see Tory MPs hold a vote on Monday before a possible online ballot for party members next week.

James Duddridge, one of Johnson's closest allies in parliament, said he had been in contact with his old boss via WhatsApp.

"He said... 'We are going to do this. I'm up for it'," the MP said, as a Sky News reporter posted a photograph apparently showing Johnson on a flight home from the Dominican Republic.

- 'Fresh start' -

The Sunak and Johnson camps are reportedly seeking talks to see if there is scope for a unity deal -- although there is plenty of bad blood since the former prime minister's defenestration.

Mordaunt, who just missed out on making the final runoff after Johnson quit, said she was running for "a fresh start, a united party and leadership in the national interest".

But polling company YouGov found that three in five voters now want an early general election, in line with demands from opposition parties, as Britons struggle with a worsening cost-of-living crisis.

Labour and other parties argue only an election can end the months of political chaos, sparked when Johnson was himself forced out after non-stop personal and political scandal.

In the resultant contest, Truss won the support of just over 80,000 Tory party members, defeating Sunak, who correctly warned that her right-wing programme of debt-fuelled tax cuts would crash the economy.

Truss announced on Thursday she was quitting after just 44 tempestuous days in office.

- 'Questions to answer' -

Political website Guido Fawkes, which is running a rolling spreadsheet of Tory MPs' declared support, had Sunak on 103, Johnson on 68 and Mordaunt on 25 by late Friday.

Defence Secretary Ben Wallace, a favourite of the Tory grassroots, told reporters he was not standing himself. "At the moment, I'm leaning towards Boris Johnson," he said.

But Wallace added that Johnson still had "some questions to answer" over the multiple scandals, which resulted in a yet-to-launch investigation in the House of Commons.

If found guilty of lying to the Commons over the "Partygate" scandal -- lockdown-breaching revels held in Downing Street -- Johnson could be suspended or even expelled from parliament.

As a result of such controversies, Johnson left Number 10 with dismal poll ratings, and other Tories were aghast at the prospect of his coming back.

Veteran backbencher Roger Gale warned that Johnson could face a wave of resignations from MPs refusing to serve under him as leader.

- 'Backstabber' -

Johnson's ambiguous appeal was underlined by a YouGov poll that found 52 percent of voters opposed to his return.

In Sunak's constituency in Yorkshire, northern England, 58-year-old farmer Elaine Stones said the party had made a mistake in electing Truss instead of him.

"He's honest, reliable and he should have been voted in last time," she told AFP.

But retiree Maureen Ward called Sunak a "backstabber" who helped to topple Johnson.

"He wielded the knife and once you do that, you can't be trusted," she said.