As both campaigns traded barbs on Saturday, Ms Truss refused to engage with Mr Sunak’s suggestion he was the “underdog” as she said she was “not taking anything for granted”.
The Foreign Secretary was in Kent where she highlighted her plans for a “red tape bonfire” of EU regulations, while Mr Sunak used a speech in Grantham, the birthplace of Margaret Thatcher, to kick-start his campaign as he bids to win over Tory members.
Ms Truss, tipped as the favoured candidate among grassroots voters and backed by Johnson loyalists, faced attacks from the former chancellor over her planned tax cuts as he sought to convince party members that he was the true Thatcherite in the contest.
Mr Sunak also took aim at his rival’s Brexit credentials in his speech on Saturday morning, which was heavy on warnings about the dangers of inflation as he promised to put the UK on a “crisis footing” if he enters No 10.
Speaking to a largely friendly crowd, he called himself the “underdog”, but stopped short of naming Ms Truss personally.
He told the crowd: “The forces that be want this to be a coronation for the other candidate. But I think members want a choice and they are prepared to listen.”
Pressed by reporters to be more specific, he said he was talking “generically”.
Elsewhere in his speech, Mr Sunak sought to create a clear dividing line between himself and Ms Truss as he implicitly criticised her proposed tax cuts, which she says will help decrease inflation.
“If we are to deliver on the promise of Brexit, then we’re going to need someone who actually understands Brexit, believes in Brexit, voted for Brexit,” he told the crowd, to cheers.
In a speech punctuated by frequent applause, he also said: “We have to tell the truth about the cost of living.
“Rising inflation is the enemy that makes everyone poorer and puts at risk your homes and your savings. And we have to tell the truth about tax.
“I will not put money back in your pocket knowing that rising inflation will only whip it straight back out.”
He called for the need for radicalism in politics, telling the crowd: “Real change is there, I swear it.”
That change includes a promised plan to tackle NHS backlogs, driven in part by a so-called “vaccines-style” taskforce.
Warning against “privatisation by the back door”, Mr Sunak announced plans to eliminate one-year NHS waiting times six months earlier than planned by September 2024, and to get overall numbers falling by next year.
Ms Truss, who told reporters in Kent that she would install a “strong” health secretary to tackle that NHS backlog, reiterated her commitment to tax-cutting policies.
“I think it is wrong to be taking money from people that we don’t need to take, when people across the country are struggling with the cost-of-living crisis,” the Foreign Secretary said.
“We know fuel bills are higher. We know that food bills are higher. And what my changes would do is help people with the cost of living, but also drive growth in the economy that’s going to lead to higher tax revenues so we can pay back that debt.”
She said she was being “honest” about the economy, hitting back at the suggestion that her plans are unrealistic.
She added: “I’m being very honest about the situation. We face the biggest economic crisis we have for a generation and now is not the time for business-as-usual.”
Ms Truss refused to get into Mr Sunak’s view that she was the clear frontrunner, telling reporters: “I want the support of Conservative members. I’m somebody who is campaigning as a Conservative and will govern as a Conservative.”
The Foreign Secretary, who has faced accusations of consciously courting comparisons with Mrs Thatcher, also waved off suggestions that the race was about who was the strongest Thatcherite.
Earlier, Mr Sunak, who was joined on his visit by daughters Krishna and Anushka, as well as wife Akshata Murthy, laughed when pressed on whether the choice of location was a coincidence, telling reporters he believes what he is proposing is “common sense Thatcherism”.
“I think we need to move on. You know, we’re in the 2020s. We’re facing a global economic crisis,” Ms Truss told reporters.
She began the weekend by announcing that if elected, she will set a “sunset” deadline for every piece of EU-derived business regulation and assess whether it stimulates domestic growth or investment by the end of 2023.
A lot of project fear-style material on Twitter today. The idea that there isn’t scope for reducing the burden of tax through both a new spending review and by putting our Covid debt on a longer-term footing as it rolls over is transparently false. (1/n)
— Simon Clarke MP (@SimonClarkeMP) July 23, 2022
Industry experts would be tasked to create “better home-grown laws” to replace those that fail the test, if they are not ditched altogether.
Both campaigns received backing from prominent supporters over the weekend, with Deputy Prime Minister Dominic Raab, a supporter of Mr Sunak, telling BBC Radio 4’s Today programme that only the former chancellor had set out a “credible” plan on the economy and on the NHS.
Ms Truss and her tax proposals were also the subject of a a vigorous defence by ally Simon Clarke, the Chief Secretary to the Treasury.
In a series of posts on Twitter, he said that it was time to “explode the myth” that cutting taxes is anti-Conservative, and hit out at what he called “project fear material”.