Mr. Cameron, speaking to the Conservative Middle East Council, an organization that promotes discussion about the region among the Conservative Party, said on Monday that showing progress toward a two-state solution was essential to negotiating peace, and called Israel’s security policies of the last three decades “a failure.”

The British government has long held the position that it would only recognize a Palestinian state at the “right time” in the peace process with Israel, and Mr. Cameron’s comments, in London, suggested that Britain may be aiming to do that sooner.