The Prime Minister has refused to answer inquiries from Mr Bryant until he apologises for misleading the House of Commons about alleged meetings between Mr Cameron and Rupert Murdoch.
But Mr Bryant used a parliamentary technique that obliged the Prime Minister to reply to his written questions on the topic on a certain day.
Mr Cameron declined to answer the substance of Mr Bryant's questions and instead referred him to a letter he has written to Labour's deputy leader Harriet Harman on related matters.
In that, he said he was happy to respond to Ms Harman's questions in full but that he was still owed an apology by Mr Bryant.
He said that Mr Bryant had misled the Commons after using inaccurate and confidential information he had obtained as a core participant of the Leveson Inquiry. In his letter to Ms Harman, Mr Cameron said briefly: "I have co-operated with the Leveson Inquiry and given them all the material they have asked for."