Labour’s leader said he did not believe the aim in the short term should be to “balance the books”.
In an interview with The Times, Sir Keir said: “Over the course of the recovery, tax rises are not the right way to ensure that we go forward to a more thriving economy.
“There’s an emerging view that I subscribe to that, in the short term, you don’t balance the books and you don’t choke off the recovery by raising taxes on the one hand or reverting to austerity on the other.”
He added: “You’ve got to get your economy to thrive.”
During the Conservative Party conference last October, Mr Sunak, the chancellor, hinted of tax rises ahead as he said governments had a “sacred duty” to balance the books.
The Telegraph reported on Saturday that the chancellor was looking at freezing personal income tax allowances in his Budget next month, in a move which could cost the average family £250 a year by 2024-25.
Millions of people may be forced to pay more in tax under the reported plans, with The Telegraph saying officials were looking into scrapping planned increases for the two lower tax thresholds.
The newspaper also reported at the end of last month Mr Sunak was considering an increase in capital gains tax.
The Treasury has been approached for comment.
Labour has also called on Mr Sunak to ease the burden of Covid-related debt on business, warning hundreds of thousands of firms could go to the wall unless the government acts.
Anneliese Dodds, the shadow chancellor, said companies were facing the prospect from next month of having to start paying back £71bn in government-backed loans intended to nurse them through the pandemic.
She said Mr Sunak’s insistence that the loans were repaid on schedule risked “crushing” any prospects of recovery under a mountain
Ms Dodds urged the government to convert the bounce back loan scheme into a “student loan-style arrangement” with firms only starting to make repayments once they are making money again.
A Treasury spokesperson said: “We know businesses need every pound to protect jobs rather than repaying loans, which is why in September we announced flexibility on repayments for both the bounce back loans and coronavirus business interruption loans schemes.”
“For bounce back loans that now means businesses can choose to make no payments on their bounce back loans until 18 months after they originally took them out.”
Additional reporting by Press Association