Mr Cameron was clarifying the issue following advice from the attorney general, who had said the government, under pressure from Europe, may need to back down over the issue of prisoner votes.
The European court of human rights has ruled, in what is known as the Scopola ruling, that there should not be a blanket ban on prisoners being allowed to vote.
Giving evidence to the justice select committee, Mr Grieve warned that Britain was obliged to obey the judgment and could face huge damages claims from prisoners.
“The issue, it seems to me, is whether the United Kingdom wishes to be in breach of its international obligations and what that does reputationally for the United Kingdom,” he said. “This is not a matter where there’s not parliamentary sovereignty. There clearly is. Parliament gives and parliament can take away.
However, Mr Cameron said during prime minister’s questions: “The House of Commons has voted against prisoners having the vote. I don’t want prisoners to have the vote, and they should not have the vote.
“If it helps by having another vote in parliament on another resolution to make absolutely clear, to help put the legal position beyond doubt, I am very happy to do that.”
In February the House of Commons voted by a margin of 234 to 22 against removing the blanket ban.