The Chancellor urged Bank Governor Andrew Bailey not to trim rates until he is "absolutely sure" high inflation is beaten.
The tug of war over what happens next to interest rates could have a massive impact on voters at the General Election, which is expected later this year, since bringing inflation down to 2% is one of Rishi Sunak's key pledges.
Mr Hunt spoke after the Bank's Monetary Policy Committee held interest rates at a 16-year high of 5.25% for the sixth consecutive meeting.
Speaking after the decision, an "optimistic" Mr Bailey offered some hope to mortgage borrowers that rates will soon be reduced. He said: "It is likely that we will need to cut the bank rate over the coming quarters."
Mr Bailey indicated cuts would be "possibly more so than currently priced into market rates".
But Mr Hunt responded that it was important policymakers did not go too fast - in order to avoid having to put rates back up again to curb inflation.
Asked if he is hoping rates will be cut ahead of the General Election, the Chancellor said he "would much rather that they waited until they're absolutely sure inflation is on a downward trajectory than rush into a decision that they had to reverse at a later stage".
Stressing that the Bank takes its decisions independently, Mr Hunt added: "What we want is sustainably low interest rates, and I think what's encouraging is that the Bank of England Governor, for the first time, has expressed real optimism that we're on that path."
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