President Obama says Israeli and Palestinian negotiators face "hard work and hard choices" in direct peace talks set to open in Washington tonight.
The meeting comes after a divided Israeli Cabinet agreed to release 104 long-term Palestinian prisoners convicted of deadly attacks.
"The most difficult work of these negotiations is ahead, and I am hopeful that both the Israelis and Palestinians will approach these talks in good faith and with sustained focus and determination," Mr Obama said in a statement.
The US president said he believed peace between the two parties was both "possible and necessary."
Israeli President Shimon Peres has formally asked Prime Minister Benjamin Netanyahu to form the next government after a majority of newly elected lawmakers recommended him to lead the country.
Mr Netanyahu has six weeks to form a governing coalition for what would be his third term as Israeli premier, but faces a challenge drawing secular and religious parties under one umbrella.
Mr Netanyahu said the government's next priorities should be to prevent Iran from building a nuclear weapon, to deal with the stockpile of weapons in the region and to make peace with the Palestinians.
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.
Palestinian protesters clashed with Israeli forces on Monday at the Qalandiya checkpoint that separates the West Bank and Jerusalem.
The protesters hurled stones towards Israeli soldiers who responded with tear gas.
There were similar scenes across the West Bank on Monday as violence continued to rage in the Gaza Strip and southern Israel.
Clashed between Palestinian demonstrators and the Israeli military also broke out in Bir Zeit, and at the Hawara crossing, near Nablus.
The Israel military said Gaza militants have fired 110 rockets on southern Israel since Saturday, the Associated Press has reported.
They said 10 rockets had been fired by midday local time today, including one that struck the back of a house in Netivot.
Israeli aircraft struck three militant sites in Gaza earlier in the day, AP reported.
Israeli officials have warned of a tough response after a Palestinian rocket fired from the Gaza Strip struck a house in southern Israel.
The rocket hit the town of Netivot, causing damage but no injuries.
The strike ended a brief overnight lull to three days of clashes, which has left six Palestinians dead, including four civilians, and 40 wounded.
Eight Israelis have also been wounded in the cross-border attacks.
The head of the Hamas government in the tiny enclave of Gaza, which lies between Israel and Egypt, said he hopes Mohamed Morsi will play a leading role in the Palestinian cause.
The streets of Gaza City were filled with cheering supporters moments after the announcement of Morsi's victory was made.
The leader of the Hamas government, Ismail Haniyeh, told Reuters: "We will look to Egypt to play a big, leading role, a historic role, regarding the Palestinian cause, in helping the Palestinian nation get freedom, return home, and totally end the Gaza siege".