David Cameron said both sides of the Israeli-Palestinian conflict will "have to take difficult and unpalatable and sometimes unpopular decisions for their constituencies" in order to achieve the peace settlement.
Speaking alongside Palestinian President Mahmoud Abbas after talks in Bethlehem, Mr Cameron said about the peace settlement: "I'm not saying it's definite or even probable, but it's certainly possible."
David Cameron is meeting Palestinian president Mahmoud Abbas today on the second day of a trip to the Middle East designed to bolster efforts to rekindle the stalled peace process.
Mr Cameron will also hold talks with one of his predecessors, former Prime Minister Tony Blair, to discuss progress on peace talks. Mr Blair is the European peace envoy of "the Quartet" of the United Nations, the EU, the US and Russia.
They are expected to meet for 20 minutes in East Jerusalem to discuss Mr Blair's Palestinian economic initiative, which aims to promote growth in the West Bank and Gaza Strip.
The Prime Minister's appeal yesterday for Israelis and Palestinians to embrace a vision of lasting peace in the region was undermined by a barrage of more than 30 rockets fired from Hamas-controlled Gaza into the south of Israel.
Palestinian President Mahmoud Abbas was given a hero's welcome on his return to Ramallah following the UN General Assembly's vote to upgrade Palestine's status from "observer entity" to "non-member state".
However, the upgrade falls short of full UN membership, which only the Security Council can grant.
In a speech broadcast on state television, he told the cheering crowds who greeted him, "Yes, now we have a state".
"Congratulations to all of you brave Palestinians; you alone have accomplished this achievement and alone have won this victory", he said.