Rishi Sunak told Sunday with Laura Kuenssberg: “I want people to be reassured that we’ve got to hold our nerve, stick to the plan and we will get through this.”
This week the Bank of England raised interest rates to a 15-year high of 5%.
Millions of people are facing higher mortgage repayments following the rise.
Meanwhile, those who rent could face higher payments or the prospect of squeezed landlords selling their property, according to the National Residential Landlords Association.
Mr Sunak continued to back the Bank of England despite some Conservatives saying it has not done enough to bring inflation back to its 2% target.
Inflation – which measures the rate at which prices are rising – remained at 8.7% in May despite the Bank raising interest rates 13 times since December 2021.
“I can tell you as prime minister, the Bank of England is doing the right thing,” Mr Sunak told the BBC. “The Bank of England has my total support. Inflation is the enemy.”