LONDON—British Prime Minister David Cameron is ducking new questions about text messages he traded with Rebekah Brooks, the former chief of News Corp.'s U.K. newspapers who faces charges linked to the country's phone hacking scandal.

Opposition Labour Party lawmaker Chris Bryant demanded Wednesday to know whether some messages had been withheld from the country's judge-led inquiry into press standards because they were "too salacious."

Cameron said Bryant had previously made untrue claims about the saga. "Until he apologizes, I'm not going to answer his questions," the prime minister said.

The inquiry did disclose some text messages involving Cameron and Brooks. Others were deemed irrelevant to the panel's role scrutinizing links between the press and the powerful in Britain.