Annual price growth in the UK, which sat at 4.6% last month, has not met the Bank's 2% target since July 2021, reaching a peak of 11.1% in October last year.
In a letter to Bank of England governor Andrew Bailey as part of the chancellor's Autumn Statement on Wednesday (22 November), he said the government was "fully committed to the Monetary Policy Committee's independence".
ECB warns high rates are pushing economy towards fragility
The letters came more than a year since former prime minister Liz Truss considered curbing the Bank of England's independence as part of her leadership bid.
Hunt also confirmed that the Asset Purchase Facility will remain in place for the financial year 2024 to 2025, "and for as long as is needed".
The Bank of England Act 1998 requires the chancellor specifies the definition of price stability and the government's economic policy objectives at least once a year.
In a letter to the BoE's Financial Policy Committee, Hunt also warned that the risk environment for the UK remained "challenging against an uncertain economic backdrop".
Federal Reserve consensus set on keeping rates higher for longer
He added: "Recent stresses in the global banking sector highlight the continued importance of maintaining robust macroprudential, regulatory and supervisory standards, and I welcome the committee's continued work to respond flexibly to such events to contribute to financial stability."
Hunt also stated that the FPC should continue to "attach a high priority" to supporting the BoE's work to address systemic risks in the market.
"As global financing conditions remain tight, the close coordination of macroprudential and monetary policy will also continue to be of heightened importance," he said.