Pointing to Mr Johnson’s record on defence spending and citing the mandate he achieved in 2019, the Cabinet minister said it was important to think about “who could win the next election” for the Conservatives.
It comes as the Tories have begun to declare their allegiances in the party’s second leadership contest in just four months, as speculation mounts over who will seek to replace Ms Truss at the helm of the party.
Supporters of Mr Johnson are backing the former prime minister to make an extraordinary political comeback, while ex-chancellor Rishi Sunak and Commons Leader Penny Mordaunt also have the public support of several MPs, should they choose to run.
An ally of Ms Mordaunt said the Cabinet minister is not currently working on a leadership bid, though she is “taking soundings” from colleagues on the prospect of her standing for the top job.
There has also been no declaration yet from Mr Sunak, who did not answer questions from reporters as he left his home on Friday morning.
Mr Johnson – who has not ruled himself in or out of the race – already had the support of Business Secretary Jacob Rees-Mogg, who tweeted a graphic saying “I’m Backing Boris” alongside the hashtag #BORISorBUST.
The post prompted a backlash from former minister Tim Loughton, who asked “how on earth” that slogan could be helpful to the party.
“I would not use the tag line #BorisandBust and you really should think this through properly if you have any interest in party unity,” he tweeted.
Levelling Up Secretary Simon Clarke and Tees Valley mayor Ben Houchen have also confirmed they would back Mr Johnson, telling The Telegraph he is “the person we need to lead our country and our party”.
But Foreign Office minister Jesse Norman argued that selecting the former PM would be “absolutely catastrophic” while veteran backbencher Sir Roger Gale, a long-time critic of Mr Johnson, warned that if he succeeds he could be met with a wave of resignations by Tory MPs.
Mr Wallace – a popular figure among party members – ruled himself out of the race, citing his commitment to the defence brief.
He argued that without national security there is “no economic security”, and said he believes it is “important” that whoever puts themselves forward for the top job indicates that.
However, Mr Wallace said he also has to “recognise the issue of the mandate”.
He told broadcasters: “This will be potentially our third prime minister since the general election of 2019 – that means we have to think about that legitimacy question that the public will be asking themselves, and also about who could win the next election – that’s obviously important for any political party at the time.”
Mr Wallace said Mr Johnson would still have “some questions to answer” as he faces an investigation by the Commons Privileges Committee over claims he lied to Parliament about lockdown parties in Downing Street.
But he said he is “leaning towards” backing the former PM to succeed Ms Truss in Downing Street, praising him for his record on investing in defence and pointing to the “huge majority” he won in 2019.
Earlier this year, Mr Johnson promised a further £55 billion in defence spending over the rest of the decade in response to the threat posed by Vladimir Putin’s Russia.
He committed Britain to increasing defence spending to 2.5% of gross domestic product (GDP), a measure of the size of the economy, by the end of the decade and encouraged Nato allies to boost their own military budgets.
Mr Wallace added that he hoped Jeremy Hunt would stay as Chancellor, describing him as “calm”, “experienced” and “knowledgeable”.
Diehard Johnson loyalist Nadine Dorries, the former culture secretary, claimed she had spoken to the former PM following Ms Truss’s resignation and hinted strongly that he was preparing to run.
“He is a known winner and that is certainly who I’m putting my name against because I want us to win the general election. Having a winner in place is what the party needs to survive,” she told Sky News.
Labour leader Sir Keir Starmer, who has called for an immediate general election, said the potential return of a man deemed “unfit for office” by his own MPs “adds insult to injury” for voters.
Other names in the frame include Suella Braverman, who was forced to quit as home secretary by Ms Truss, and International Trade Secretary Kemi Badenoch – both of whom stood in the last contest – although they may struggle to get the nominations.
Under the rules set out by Sir Graham Brady – the chairman of the backbench 1922 Committee – and party chairman Sir Jake Berry, nominations will close at 2pm on Monday.
The first ballot of MPs will then be held between 3.30pm and 5.30pm on Monday – if there are three candidates with the required number of nominations, the loser will be eliminated.
Once there are two candidates remaining, an indicative vote will be held so that the party membership know which is the preferred option among MPs.
Members will be able to take part in an online vote to choose their next leader and the country’s prime minister with the contest due to conclude by October 28.
The rules appear designed to encourage the candidate who finishes second to stand aside for the winner, ensuring the new leader has the support of the majority.