The former Chancellor moved to burnish his credentials by describing how he defied warnings that his career would be over to support Leave at the referendum.
While he did not mention Ms Truss by name, critics have been pointing out that the Foreign Secretary endorsed Remain six year ago – even though she is now taking a tough line on Brussels.
The jibe came as the five surviving candidates gear up for a make-or-break TV debate tonight, ahead of the next round of voting by MPs tomorrow.
Mr Sunak has topped the ballots so far and looks set to go into the head-to-head run off ballot by Tory members, but there is a huge struggle for the other spot in the final contest.
Trade minister Penny Mordaunt has been amassing significant support in second place, but she has been facing intense questions about her stance on gender issues.
Meanwhile, Ms Truss has been appealing for right-wingers to unite behind her – and Kemi Badenoch has also been putting in a strong showing. Ms Badenoch has been boosted by a ConservativeHome survey suggesting she is the favourite of activists.
Although foreign affairs committee chair Tom Tugendhat appears to have the least backing from MPs in the remaining field, he was seen as performing well in the first debate on Friday night.
Rishi Sunak (pictured in Teeside on Friday) has moved to burnish his credentials by describing how he defied warnings that his career would be over to support Leave at the referendum
Trade minister Penny Mordaunt (left) has been amassing significant support in second place, but Liz Truss (right) has been appealing for right-wingers to unite behind her
HOW THE TORY LEADERSHIP RACE WILL BE FOUGHT
Tonight: ITV hosts the second televised debate between leadership candidates.
Tomorrow – A third ballot of Tory MPs will be held which will see the candidate with the lowest number of votes eliminated.
Tuesday – More ballots will be held for the rest of the week until the list of contenders is whittled down to a final two.
Tuesday night – Sky News hosts the third and final leadership debate.
21st July – MPs will head away from Westminster for their summer break, meaning this is the deadline for a final pairing to be decided in the parliamentary stage of the leadership election.
Late July and August – CCHQ will assume responsibility for leadership election and will send out ballot papers to around 200,000 Conservative Party members. The Tory grassroots will be asked to decide between the final two candidates, with hustings events to be held across the UK.
5th September – The result of the membership ballot is announced, with the candidate receiving more than 50 per cent of the vote being declared the new Tory leader and Boris Johnson’s replacement as Prime Minister.
6th September – The new Tory leader is likely to be formally appointed as PM during a visit to the Queen at Buckingham Palace.
7th September – The new PM is set to be quizzed in the House of Commons in their first ever Prime Minister’s Questions.
In a fresh pitch to win over Brexiteers, Mr Sunak has promised to scrap hundreds of remaining EU laws and regulations if he wins the keys to No10.
He would appoint a Brexit minister to go through the 2,400 EU laws still on the statute book, and recommend which should be scrapped or overhauled within 100 days of Mr Sunak entering No 10.
In an article for the Sunday Telegraph, Mr Sunak stressed that he had always backed Brexit even though he had been warned it could damage his political career.
‘I was advised by people I respected not just that leaving the EU was a bad idea for Britain; they also warned me that backing Brexit would mean the end of my political career,’ Mr Sunak said.
‘I listened to the advice, took it seriously, and weighed my decision carefully. But none of it altered my conviction that Britain would be better of f outside the EU, unshackled from its low-growth, bureaucratic mindset.’
Mr Sunak said: ‘We need to capitalise on these opportunities by ditching the mass of unnecessary regulations and low-growth mentality we’ve inherited from the EU.
‘I have a plan, if elected prime minister, to have scrapped or reformed, by the time of the next election, all the EU law, red tape, and bureaucracy still on our statute book that is holding back our economy.
‘As prime minister, I would go further and faster in using the freedoms Brexit has given us to cut the mass of EU regulations and bureaucracy holding back our growth.
‘If we do this, we can get our economy growing quickly again and become the most prosperous country in Europe.’
The review would include an overhaul of the remaining EU financial services regulations with a view to triggering a ‘Big Bang 2.0’ for the City to enable it to maintain its status as a leading world financial centre.
Mr Sunak also indicated that he would overhaul EU General Data Protection Regulation (GDPR) rules and speed up the clinical trials by cutting EU red tape.
The latest ConservativeHome poll shows Ms Badenoch on 31 per cent – with Ms Truss, Ms Mordaunt and Mr Sunak bunched together on around 20 per cent. Although the survey is not scientific it is closely watched by MPs and ministers.
Mr Sunak topped the first two rounds of voting by MPs, although he still remains short of the 120 votes needed to guarantee him a place in the final run-off ballot.
In an interview with the Sunday Telegraph, Ms Truss said she would seek to abolish ‘Stalinist’ housing targets – unpopular with some Tory MPs – if she was elected.
‘I want to abolish the top down Whitehall inspired Stalinist housing targets. I think that’s the wrong way to generate economic growth,’ she said.
‘The best way to generate economic growth is bottom up by creating those incentives for investment through the tax system, simplifying regulations.’
Kemi Badenoch has also been putting in a strong performance and has been boosted by a ConservativeHome survey suggesting she is the favourite of activists
Foreign affairs committee chair Tom Tugendhat appears to have the least backing from MPs in the remaining field, but he was seen as performing well in the first debate on Friday night