"The Sri Lankan government needs to go further and faster on human rights and reconciliation," Cameron told a press conference at an ongoing Commonwealth summit in Colombo.
"I accept it takes time but I think the important thing is to get on the right track," added Cameron who paid an historic visit on Friday to the island's war-torn north.
"This issue is not going to go away, it's an issue of international concern."
The UN and rights group say as many as 40,000 civilians may have been killed in the final stages of the civil war in May 2009.
However Sri Lankan President Mahinda Rajapakse has denied any civilian was killed.
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He has also blocked all calls for an independent probe into claims of war crimes committed by government forces against the Tamil population in the northern Jaffna region.
Cameron said Rajapakse wanted more time to address the claims but put him on notice to deliver by March or else he would push for an international investigation through the auspice