He was referring to a recent High Court decision to uphold a ban on a Christian couple becoming foster parents after they admitted that they would refuse to tell a child that homosexuality is acceptable.
Pentecostal Christians Eunice and Owen Johns, of Derby, say they are considering an appeal over the High Court verdict.
Speaking in Derby, where he held a Cabinet meeting yesterday, Mr Cameron backed the decision.
He told the Derby Telegraph: “This matter was decided by a court in the appropriate way and I think we should rest with the judgment that was made.
The prime minister said that he was a churchgoer but added: “I think Christians should be tolerant and welcoming and broad minded.”
A spokesperson for the Johns said Mr Cameron’s comments were “lacking in any understanding of the critical situation and conflict between the two groups involved”.
The Johns are the latest in a series of Christian couples to unsuccessfully challenge equality legislation.
Earlier this year, a couple who own a hotel in Cornwall were ordered to pay £3,600 to a gay couple they refused a double room to.
Peter and Hazelmary Bull, the owners of the Chymorvah Private Hotel, argued that their Christian beliefs meant they could not allow two men to share a bed.