The bishop, Dr Alan Smith, has led Church of England criticism of the machines, which can theoretically allow users to gamble up to £18,000 in an hour.
Gambling charities would like the maximum amounts to be reduced. But reports last month suggested that the Treasury opposed the move, because of the impact it would have on tax receipts.
In his letter, however,, Hammond denied that this was the case: "Recent media reports on the status of the review of gaming machines and social responsibility measures are entirely without foundation.
"Both I and my department fully support [the department for digital, culture, media & sport's] work to ensure the UK’s gambling regime continues to balance the needs of vulnerable people, consumers who gamble responsibly, and those who work in this sector."
The DCMS is carrying out a review into gambling, announced last autumn. As well as fixed-odds betting terminals, the review is examining the impact of advertising – spending on which has doubled in the last five years.
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