Boris Johnson has instructed senior officials to plan a “meaningful ministerial meeting” with devolved governments on cost-of-living support.
Nicola Sturgeon has demanded a meeting with UK ministers to discuss help for households as prices soar.
In a letter to Mr Johnson on Monday, the Scottish First Minister said an emergency meeting, scheduled for September, cannot wait and must happen immediately.
Mr Johnson has now written back to Ms Sturgeon, saying: “I agree that the response to these pressures will be best served by the UK and devolved governments working collaboratively to navigate these challenges together.”
He has asked his permanent secretary for the union to “continue working with your officials to plan for a meaningful ministerial meeting with heads of devolved governments to consider how best to further support hardworking families”.
It is not known when a meeting will take place.
The Prime Minister and Chancellor Nadhim Zahawi met with energy bosses on Thursday to discuss rocketing bills.
Mr Zahawi has said new cost-of-living measures will be prepared for the incoming prime minister to introduce in September.
Mr Johnson added: “The Government understands that people across the UK are worried about the rising cost of living and are seeing their disposable incomes decrease as they spend more on the essentials.”
In May, the UK Government announced support worth £15 billion targeted at the most vulnerable people.
In her letter, Ms Sturgeon wrote: “This situation is fast deteriorating and many people across the UK simply cannot afford to wait until September for further action to be taken.
“I am therefore writing to seek an emergency meeting of the Heads of Government Council and propose that we, as leaders of our respective governments, meet as soon as possible this week to discuss and agree urgent steps to help those in most need now, and also formulate a plan of action for the autumn and winter ahead.”
Ms Sturgeon added that “action is needed now to address significant gaps in help for households”.
Earlier on Friday, Scotland’s Deputy First Minister John Swinney claimed the UK Government is holding the public “to ransom” by ruling out further cost-of-living measures until a new prime minister is appointed next month.