Rishi Sunak has formally entered the Tory leadership contest, promising he would lead with “integrity, professionalism and accountability” in an apparent attempt to contrast himself with his predecessors as his backers warned a Boris Johnson comeback would be a “guaranteed disaster”.

Mr Johnson’s supporters have downplayed the fact he is lagging behind his former chancellor in public support from MPs, saying he is “clearly” running, although he has not officially declared this.

However, sources close to fellow leadership hopeful Penny Mordaunt disclosed that the former prime minister has spoken to her and asked her to stand aside and to join his campaign.

The PA news agency understands that she refused, telling him that most of her support would switch to Mr Sunak if she did.

The disclosure is likely to heighten suspicions at Westminster that Mr Johnson is struggling to attract the level of support from fellow Tory MPs he hopes for.

Mr Sunak, becoming the second candidate to enter the race after Ms Mordaunt, said he wants to “fix our economy, unite our party and deliver for our country” at a time of “profound economic crisis”.

He said in a statement: “I served as your chancellor, helping to steer our economy through the toughest of times.

“The challenges we face now are even greater.

“But the opportunities, if we make the right choice, are phenomenal.

“I have the track record of delivery, a clear plan to fix the biggest problems we face and I will deliver on the promise of the 2019 manifesto.

“There will be integrity, professionalism and accountability at every level of the government I lead and I will work day in and day out to get the job done.”

Mr Sunak on Sunday gained several more valuable backers in new Home Secretary Grant Shapps, Work and Pensions Secretary Chloe Smith and two influential figures on the Tory right – Suella Braverman and Northern Ireland minister Steve Baker.

Tory big beast Mr Shapps, who also threw his weight behind Mr Sunak in the last leadership contest against Liz Truss, tweeted that the ex-chancellor would “provide stability and proven economic competence in these challenging times”.

Ms Braverman, who was briefly home secretary under Ms Truss, said that while she had previously “backed Boris,” the country is in “dire straits now” and needs “unity, stability and efficiency”.

“Rishi is the only candidate that fits the bill,” she wrote in the Telegraph.

Mr Baker, the former head of backbench Brexiteers, was scathing in his assessment of a potential comeback by Mr Johnson, who is mulling a bid to return to the top job just months after being forced out by his own MPs.

He told Sky’s Sophy Ridge On Sunday: “Boris would be a guaranteed disaster.

“There’s going to be a vote before the House of Commons on this issue of privileges, whether he will deliberately misled the house.

“In that vote it’s guaranteed there’ll be a large number of Conservatives who will refuse, as they see it, to lay down their integrity to save him, and at that moment his premiership will collapse.”

Mr Johnson is to face an inquiry into whether he lied to the Commons over the partygate scandal, for which he was fined by police.

If found guilty by the Commons Privileges Committee, he could face recall proceedings that would leave him battling for his seat in the Commons if he receives a suspension of 10 days or more.

“I’m not willing to lay down my integrity for Boris Johnson,” Mr Baker said.

Conservative former cabinet minister Dominic Raab also warned that the partygate probe would overshadow a Mr Johnson premiership.

He told BBC One’s Sunday With Laura Kuenssberg programme: “In a matter of days, not weeks, he’s going to see televised witness testimony, including his own, which is going to take him right back into that spiral.”

But Mr Johnson on Sunday gained the backing of Foreign Secretary James Cleverly and Nadhim Zahawi, the Chancellor of the Duchy of Lancaster.

Mr Zahawi said the ex-Prime Minister “got the big calls right” and argued “Britain needs him back”.

He tweeted: “When I was Chancellor, I saw a preview of what Boris 2.0 would look like. He was contrite and honest about his mistakes. He’d learned from those mistakes how he could run No 10 and the country better.”

Mr Zahawi, who joined other Cabinet ministers including Ben Wallace, Anne-Marie Trevelyan and Jacob Rees-Mogg in backing their former boss, had urged him to resign as prime minister in July.

Mr Cleverly similarly said that Mr Johnson “has learned lessons from his time in No10”.

Labour’s shadow communities secretary Lisa Nandy told Ridge: “It’s extraordinary watching Tory MPs who put in letter of no confidence in him just a few weeks ago saying he wasn’t fit to hold the highest office now talking openly about trying to bring him back. It is a sign of absolute utter desperation in the Tory party.”

Mr Rees-Mogg, the Business Secretary, confirmed Mr Johnson intends to run, telling Kuenssberg: “I have been speaking to Boris Johnson, and clearly he’s going to stand, there’s a great deal of support for him.”

Fellow Johnson ally Sir James Duddridge gave a similar indication and suggested the former prime minister will “cooperate fully” with the partygate probe.

The Tory MP tweeted: “Boris on good form at the 8am meeting with MPs. In a first for Boris he was rather smartly dressed!

“He made it very clear the Privileges Committee must and will be allowed to get on with their process. He will cooperate fully.”

Ms Mordaunt, the first candidate to declare, insisted she is “in this to win it” despite being far behind her potential rivals on public endorsements.

She has just 23 to Mr Johnson’s 46 and Mr Sunak’s 127, according to a PA tally.

Ms Mordaunt said she was a “halfway house” between Ms Truss and Mr Sunak in the last contest and that she is “best-placed to unite our party”.

“I’m in this to win it. I think it’s important for our party, we have a contest. I am very confident about our numbers,” she told Kuenssberg.

But the leadership hopeful refused to give any details of her tax and spend policy, declining to explicitly commit to raising benefits in line with inflation, the pensions triple lock, 3% defence spending and no cuts to the health service.

“I’m not going to be drawn into the detail,” she repeatedly said.

She said reports that she offered to back Mr Johnson in return for a job from him were “completely false” and refused to say which of her two rivals she would back.

It came after Mr Johnson and Mr Sunak were said to be locked in talks late into Saturday evening amid speculation over whether the pair could agree on a joint ticket.

Mr Johnson returned to the UK on Saturday to plot a second run for the top job, in a move that has divided opinion among Conservative MPs including his former allies.

He arrived at Gatwick Airport with his family after breaking off a holiday in the Dominican Republic following Ms Truss’s dramatic resignation on Thursday.

Labour leader Sir Keir Starmer criticised the “ridiculous, chaotic circus” taking place at the top of the Conservative Party as he repeated his call for a general election.

Tory MPs will vote on Monday, and two candidates will be put forward to the party membership unless one pulls out, with a result being announced on Friday.

Candidates have until 2pm on Monday to secure the 100 nominations, limiting the ballot to a maximum of three candidates.

Supporters of Mr Johnson believe that if he can make it to the last two, he will win in the final online ballot of party members with whom he remains popular.

Some MPs have warned they would resign the Tory whip and sit in the Commons as independents if Mr Johnson returned to Downing Street.