Boris Johnson won't introduce big tax and spending measures before he leaves office to ease the cost-of-living crisis, according to a report.
Tony Danker said it made no sense to wait for the next prime minister.
The first minister of Scotland called for an urgent meeting.
The public was facing challenging times, according to the office of the prime minister.
The spokesman for Mr Johnson said it was up to his successor to decide on further help.
It is not for the prime minister to make major fiscal interventions during the period after Mr Johnson leaves office.
The government is working on cost-of-living issues, according to the Cabinet Office minister.
When the new prime minister arrives, the plan is in place for them to put their foot on the pedal, he said.
He argued that holding a meeting of the government's emergency response committee would be a political act.
The cost-of-living crisis was alleviated by a £15 billion package of support.
The discount on energy bills was one of the things that was given to households.
The government is under increasing pressure to do more.
The Bank of England predicted last week that the UK would be in a recession.
The energy price cap will go up in October, and industry analysts think the average domestic energy bill will be more than 3,600 a year.
Mr Danker, head of the Confederation of British Industry (CBI), said the prime minister and the candidates for the Conservative leadership should come together to agree a common pledge to support people.
He said that the economic situation people and businesses are facing requires all hands to the pump.
While the leadership contest plays out followed by a slow start from a new prime minister and cabinet, we can't afford a summer of government activity.
The civil service should be directed by the prime minister to draw up options for helping the most vulnerable people, and these should be made available to both leadership candidates, according to the business group.
Ahead of Ofgem's announcement of the next energy price cap, Mr Johnson, Mr Sunak and Ms Truss should agree a way forward to support people and businesses with energy bills.
Ms Sturgeon has called for an emergency meeting with Mr Johnson and the leaders of the devolved governments to discuss ways to help people.
She told the prime minister that the government couldn't respond on the scale required without the government taking action.
Mr Brown urged Mr Johnson, Mr Sunak and Ms Truss to agree an immediate Budget to prevent a winter heating catastrophe.
The emergency committee should be in permanent session to deal with the fuel and energy crisis, according to him.
The prime minister is on holiday, the chancellor is on holiday, and the two leadership candidates for prime minister are campaigning.
No 10 said it was up to Mr Johnson's successor to decide on further support for households.
The spokesman said that Mr Johnson and his Chancellor would be meeting this week to discuss progress on the support measures.
The shadow chancellor said that people are worried about how they'll pay their bills and that the prime minister does not seem to care.
Labour would scrap tax breaks on oil and gas producers and give more help to people who are struggling to pay their energy bills if it were to win the leadership race.
The two MPs trying to take over the leadership have been at odds with each other.
Mr Sunak said that the plans of his opponent would not touch the sides.
The supporters of Ms Truss said her proposed tax cuts would help people.