It follows No 10's disclosure late on Monday that Patrick Rock resigned last month after officials were made aware of a potential offence. He was subsequently arrested and is now under investigation by the National Crime Agency.
Mr Rock, 62, who was deputy head of the Downing Street policy unit, was previously the subject of a complaint of alleged "inappropriate behaviour", according to No 10.
Mr Cameron said: "Obviously, when I heard these allegations I was profoundly shocked and remain profoundly shocked.
"I have to be careful about what I say about this issue because a criminal investigation is under way. He did play an important role at Downing Street and he's resigned that position."
No 10 said it was first made aware of the alleged offence regarding child abuse imagery on February 12 and it was referred to the National Crime Agency and Mr Rock resigned.
Mr Rock was arrested early the following day at home in London.
Defending the delay in releasing the information, Mr Cameron said: "I don't think it would be right to pre-emptively brief out a criminal investigation and that's why we did not do that.
"But as soon as questions were asked, as questions would inevitably be asked, we have given very full and straightforward answers, which is absolutely the right way to answer this.
"I have been very clear we must handle this in an absolutely correct way and I am satisfied that is what No 10 Downing Street has done."
Mr Cameron's official spokesman later said that the earlier allegation was "in no way related to the arrest".
"The issue was appropriately resolved with the consent of and in consultation with the individual who raised the issue," said the spokesman.
Asked if Mr Cameron was aware of the complaint of inappropriate behaviour at the time it was made, the spokesman said: "The Prime Minister is always kept informed about relevant staff issues."
Mr Rock has been close to Mr Cameron for many years - the two men worked together as advisers to Michael Howard when he was home secretary in the 1990s.
Mr Rock had been involved in drawing up Government policy on internet porn filters.