The prime minister repeated his desire for a "thorough" investigation into the row that forced the resignation of chief whip, Andrew Mitchell, after another Scotland Yard officer was arrested.
The 46-year-old from the Diplomatic Protection Group was held at his workplace in central London on suspicion of misconduct in public office.
Andrew Mitchell was forced to resign over the affair
The man was not present at the time of the spat between Mitchell and officers on duty outside Downing Street last September, disputed details of which were subsequently leaked.
Speaking in Liberia, where he is attending a UN meeting on international development, Cameron said: "There is an ongoing police investigation, so it wouldn't be right for me to comment.
"All I would say is it is very important that this investigation is thoroughly carried out and proper answers are delivered."
Three weeks ago Metropolitan Police commissioner Sir Bernard Hogan-Howe said that a file of evidence on the case could be handed to the Crown Prosecution Service by the end of this month.
However, the force said yesterday that "ongoing developments" had delayed an interim report.
Investigators have taken statements from all 800 officers in the Diplomatic Protection Group (DPG) as part of the inquiry.
Two other men have been arrested so far. A 52-year-old Pc who is also from the DPG was held on suspicion of misconduct in public office and bailed until a date in February.
A 23-year-old was arrested on suspicion of intentionally encouraging or assisting the commission of an indictable offence and also released on bail.
Four other constables in the unit, which is responsible for protecting Government officials and diplomats, have been placed on restricted duty over misconduct claims.
Mitchell has admitted swearing at police, but denied calling them "plebs". He has claimed to be the victim of a deliberate attempt to "toxify" the Tories and ruin his career.
A report from the Commons Home Affairs Committee today suggested that the IPCC should be investigating the "plebgate" allegations.
Asked on BBC Radio 4's Today programme whether it should be investigating, the watchdog's chair Dame Anne Owers said: "If we had been able to get involved at the right time, yes."
But she said that the decision was taken not to launch an independent investigation because "there was already a police investigation under way".
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