The deputy prime minister, Dominic Raab, has questioned Liz Truss’s record in government, as the acrimonious Conservative party leadership race that has set cabinet colleagues against each other enters a critical 72 hours.

Tory MPs will hold up to three rounds of voting this week to narrow the field to two, leaving grassroots members to make the final choice by 5 September.

Truss has announced unfunded tax cuts worth up to £30bn, setting herself against the frontrunner, Rishi Sunak, who has said he wants to tackle inflation before cutting tax.

Raab, a Sunak supporter, said on Sunday: “Liz can answer for her policies and her record; she was chief secretary of the Treasury. People can see whether spending and headcount in the civil service went up or down.”

“Did she cut taxes at that time?” he added, speaking to Sophy Ridge on Sky News.

Truss was Treasury chief secretary between 2017 and 2019. The role involves overseeing the government’s spending plans, though the broader direction would have been set by the then chancellor, Philip Hammond.

Truss said this weekend she would ditch “Stalinist” housing targets in favour of using tax and other incentives in “opportunity zones” to encourage developers to build homes. “The best way to generate economic growth is bottom-up, by creating those incentives for investment through the tax system, simplifying regulations,” she told the Sunday Telegraph.

Tax and spending has been the key battleground in the contest, however, with most candidates promising tax cuts, while Sunak positions himself as the guardian of fiscal responsibility. He has said repeatedly he will not tell his colleagues “fairytales” about what is achievable.

Raab hammered that message home on Sunday. “Sensible Conservative economics means you get inflation down. If not, any money that is delivered to people in their bank accounts through tax cuts will be robbed again, by inflation or interest rates and mortgage payments going up. That can’t be right,” he said.

In an attempt to appeal to Brexiters, Sunak promised this weekend to review all EU law retained on the statute book by the time of the next general election, and cut red tape.

“We need to capitalise on these opportunities by ditching the mass of unnecessary regulations and low-growth mentality we’ve inherited from the EU,” he said in the Sunday Telegraph.

Penny Mordaunt, who came second in the first two rounds of voting among Tory MPs, appeared to suggest she would loosen Sunak’s fiscal rules in order to afford the tax cuts she is promising – a halving of fuel duty and an increase in personal tax thresholds.

Asked about the two current rules – that debt should be falling as a proportion of GDP in three years’ time, and that the government should only borrow to invest – Mordaunt said: “I’ve said I’d do the first.”

She added: “This is not about rewriting an entire manifesto. All of us stood on a manifesto which we have yet to deliver. And we’ve also not yet delivered on the 2016 referendum.”

Ditching the second fiscal rule would imply a laxer approach to public spending than that adopted by Labour under Jeremy Corbyn.

Speaking on the BBC’s Sunday Morning, Mordaunt also hit out at “smears” and the “toxic politics” of the contest, as she sought to rebut claims she has been misleading about her stance on trans rights.

“This is the type of toxic politics that people want to get away from: the poor British people have months of this to go,” she said, adding: “There’s a number of smears going on in the papers. My colleagues are very angry and upset that this is how the leadership contest is being dragged down.”

Documents leaked to the Sunday Times suggested Mordaunt was prepared to remove some, though not all, of the medical requirements for individuals opting to change their gender.

Her successor as equalities minister, Kemi Badenoch, also running for the leadership, has said Mordaunt’s stance in the past was to push for self-identification. That contradicts Mordaunt’s insistence in Friday’s Channel 4 debate that she was “never in favour of self-ID”.

Badenoch told the Sunday Times: “I’m not going to call her a liar, I think it’s very possible she genuinely did not understand what she was signing off. It’s a very complex area.”

Tom Tugendhat, who came fifth in Thursday’s round of voting, insisted he had the experience to be prime minister despite not having served in a cabinet post; and described Boris Johnson’s account of events in Downing Street during Partygate as “rather more fictional than reality”.