Rachel Reeves has indicated that the government could agree above-inflation pay rises for teachers and other public sector workers, saying there is “a cost to not settling” pay negotiations.

The chancellor, who did not dispute reports that independent pay review bodies for teachers and NHS staff had advised increases of about 5.5% – higher than the current 2% inflation rate – said she would set out full details later in July.

While Reeves’s tone will be welcomed by unions, the cost of such rises, with the Institute for Fiscal Studies (IFS) estimating that a 5.5% increase across all public sector professions would cost about £10bn, would place huge pressure on the government’s tight fiscal rules.

Speaking to BBC One’s Sunday with Laura Kuenssberg programme, Reeves said she was willing to make tough decisions neglected by the last government, saying the pay recommendation for teachers had been sitting unaddressed on the desk of the previous education secretary, Gillian Keegan.

“At the moment, we are looking at these pay review body recommendations, doing the analysis,” Reeves said. “We will work with public sector workers on that. And later this month we will make announcements around public sector pay when we do that full analysis of the public finances and public spending.

“But we also know that there is a cost to not settling – a cost of further industrial action, a cost in terms of the challenge that we face in recruiting retaining doctors and nurses and teachers as well. But we’ll do it in a proper way. Make sure that the sums add up.”

According to IFS estimates reported in the Sunday Telegraph, paying an extra 5.5% to teachers and nurses would cost £5.5bn, rising to about £10bn if the same increase took place for all public sector staff.

Acknowledging that she faced “huge spending pressures”, Reeves also hinted that the government would take account of the independent status of the pay review bodies, rather than often rejecting their recommendations, as sometimes took place under the Conservatives.

She said the government would do things “in a proper way”, highlighting the need for greater economic growth to improve the fiscal situation.

Jeremy Hunt, the shadow chancellor, told the BBC it was “absolute nonsense” for Reeves to suggest Labour had inherited a particularly terrible economic situation and rejected the idea that the Conservatives had dodged difficult decisions.

“You have interviewed me on many occasions over the years and you can criticise me for many things, but not taking tough and difficult decisions is one thing I don’t think people would level at me,” Hunt said, while not denying that his government received the teachers’ pay review recommendation before the election was called.

On Sky’s Trevor Philips on Sunday show, James Murray, a junior Treasury minister, refused to be drawn on what would be done about public sector pay, beyond saying Reeves would “set out our response in the context of the public finances and the public spending inheritance that we have in government”.

He added: “I think what’s not helpful for me to do for any worker in the public sector is for me to pre-empt the process that we are going through right now.”

Reeves refused to say when or if ministers may abolish the two-child limit on working age benefits, a key driver of child poverty about which Keir Starmer faces a looming backbench rebellion, saying it was impossible without knowing where the £3bn annual cost would come from.

“I am going to run our economy with iron discipline, bringing back stability, because we haven’t had stability,” she said.

Reeves lambasted what she called the inaction of the previous government, citing the example of Keegan. “The Conservative former education secretary, she had the pay review body recommendation for teachers on her desk when she was in office.

“She didn’t do anything about it. She didn’t publish it. She didn’t say how she was going to respond to it. They called an election. They didn’t make the tough decisions. They ran away from them.”

Similarly, Reeves said, a planning decision on an energy infrastructure project was ignored because the then energy secretary, Claire Coutinho, “wasn’t willing to make those difficult decisions”.