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."
The Prime Minister also held brief talks with his Labour predecessor as premier, Tony Blair, who is now the special envoy of the Quartet of the UN, US, EU and Russia, working on the development of the Palestinian economy.
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.
The Arab League endorsed Palestinian President Mahmoud Abbas's rejection of Israel's demand for recognition as a Jewish state, as U.S.-backed peace talks approach a deadline next month.
The US want Mr Abbas to make the concession as part of efforts to reach a "framework agreement" and extend the talks aimed at settling the Israeli-Palestinian conflict.
Benjamin Netanyahu has been Israel's first prime minister to make recognition of his country as a Jewish state a requirement for peace.
Palestinian Prime Minister Salam Fayyad has resigned, leaving the country without one of its most moderate voices, Reuters reported.
President Mahmoud Abbas met with Fayyad today and accepted his resignation, thanking him from his service, the official Palestinian news agency Wafa said.
According to the statement, Abbas asked Fayyad to continue to continue in his post until he forms a new government.
The president is expected to name a new prime minister within days, Reuters reported, citing unnamed Palestinian officials.
President Barack Obama reaffirmed his commitment to creating an independent Palestinian state saying "simply, Palestinians deserve a state of their own".
Obama said he has told Israeli Prime Minister Benjamin Netanyahu that continued Jewish settlement activity was not constructive and did not "advance the cause of peace".
Speaking at a joint news conference with Palestinian President Mahmoud Abbas, Obama said he had not lost hope in achieving a two-state solution.
However, the President offered no new proposals to getting there.
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.
The Palestinian President Mahmoud Abbas has urged the UN General Assembly to "issue a birth certificate" for the state of Palestine.
The United Nations is expected to vote tonight and take a step towards recognising a Palestinian state.