The group of families is expecting the inquiry to be published by the end of 2015, otherwise they will take a legal action against Chilcot.
"My argument would be: ‘You have had plenty of time now, you have got to get on with it, set a date for publication and let’s put this past us’," Cameron told the BBC Radio 4.
The prime minister admitted he had no power to order the report to be published, as it is an independent inquiry.
Cameron, however, stressed the need for the report be published because parents of those killed in Iraq want to know the answers before the end of their own lives.
"So they are immensely frustrated and I share their frustration," the prime minister added.
In February, Chilcot announced that the report would be delayed over the declassification of conversations between then UK Prime Minister Tony Blair and former US President George W. Bush. Chilcot pointed out the scope and complexity of the inquiry as additional reasons for the delay.
The United Kingdom was part of the US-led coalition that invaded Iraq in 2003 after accusing Iraq's then-leader Saddam Hussein of backing terrorism and possessing weapons of mass destruction. The claim has turned out to have been false, based on the inaccurate interpretation of fraudulent evidence.
According to the UK Defense Ministry, 179 UK soldiers died in the Iraq War.