Theresa May refused to back Michael Fallon, the defence secretary, yesterday after he had claimed that high earners would not face income tax rises under a new Conservative government.

Fallon said in an interview that “the only way” for higher-rate taxpayers to “be sure their taxes won’t rise is to vote Conservative”. In contrast, the Tory manifesto only pledged to keep taxes “low” and did not rule out income tax rises. When the prime minister was pressed to confirm Fallon’s claim she declined, and said only that the Tories had a “firm intention” to reduce taxes.

Jeremy Corbyn said her comments showed there was “complete chaos” in the Tory leadership, while Vince Cable, the former Liberal Democrat business secretary, said May would probably introduce “stealth taxes” including national insurance rises.

Yesterday’s exchanges over tax came after a difficult period for May. Yesterday’s campaigning began with former Tory leader Iain Duncan Smith admitting that she had been “on the back foot”.

The prime minister, who has been accused of going missing during the campaign for failing to appear in the television leader debates, faced journalists at a press conference in West Yorkshire.

She was asked about Fallon’s interview with the Daily Telegraph in which he said: “You’ve seen our record. We’re not in the business of punishing people for getting on. On the contrary, we want people to keep more of their earnings. The only way they can be sure their taxes won’t rise is to vote Conservative.”

But May refused to depart from her manifesto. “Our position on tax hasn’t changed,” she said. “We have set it out in the manifesto. It is our firm intention to reduce taxes for ordinary working families.”

That prompted a retort from Corbyn, who was in Lincoln. “One minister says they’re going to give no more tax rises, indeed possibly tax reductions for the very wealthiest, then they can’t answer the question about tax rises for the rest of the population, then they can’t answer the questions about funding social care.”

Cable said: “Since they are ruling out increases in income, corporate tax and VAT, we must assume that there will be an increase in national insurance and in various ‘stealth taxes’ yet to be specified.”

He added: “Both Labour and the Conservatives are adopting a Brexit strategy that seems explicitly designed to inflict maximum economic damage. The storm clouds are already gathering – we are seeing rising inflation, falling real wages and rising personal debt.

“Only the Lib Dems have a positive economic plan, including boosting spending while still achieving a surplus on the current budget. Theresa May keeps insisting that no deal is better than a bad deal, but an extreme Brexit could be disastrous.”

Meanwhile Nicola Sturgeon toured Scottish constituencies by helicopter. She said Scots had a “golden opportunity” to end austerity across the UK and “determine the size of Theresa May’s majority”. Sturgeon said: “The Tories’ austerity agenda has failed on every count – not only has it choked off the economic recovery, but the years of underinvestment have put huge pressure on public services across the UK.

“We simply can’t go on with more of the same, but that is exactly what the Tories are planning to do – and this snap election has presented a golden opportunity for voters across Scotland to say enough is enough. With polls tightening across the UK, the votes of people across Scotland could determine the size of Theresa May’s majority.”

The Scottish Tory leader Ruth Davidson said the election was “the last chance we’ll have to stop Nicola Sturgeon in her tracks.”

Nigel Farage said he felt “a degree of vindication” after hearing that prosecutors had brought charges against Craig Mackinlay, the Conservative candidate who defeated him in South Thanet in 2015. Mackinlay, who says he is confident he will be cleared, is one of three people to be prosecuted over allegations relating to election spending in his battle with Farage.