Mr Netanyahu greeted Mrs Clinton and Mr Abbas against a backdrop that included a Palestinian flag US Secretary of State Hillary Clinton is due to meet Palestinian leader Mahmoud Abbas in Ramallah, amid renewed Middle East peace talks in the region.
At the end of two days of negotiations, Mr Abbas again said he would walk out of the talks if a partial Israeli ban on settlement building was not renewed.
Despite the ultimatum, US officials insisted that progress was being made.
Meanwhile, Israeli warplanes conducted two separate raids in Gaza, following Palestinian rocket and mortar attacks.
There has been an upturn in violence since the peace talks, which resumed two weeks ago after a 20-month gap.
Israeli and Palestinian leaders made “progress” on the issue of Jewish West Bank settlements during Wednesday’s talks in Jerusalem, US envoy George Mitchell said, without elaborating.
Israel has so far refused to renew the restrictions, which are due to expire on 26 September.
But Mr Mitchell said the two leaders had tackled the issues at the heart of their decades-old conflict – Israel’s security, the borders of a future Palestinian state, the fate of Palestinian refugees and the status of Jerusalem.
“The two leaders are not leaving the tough issues to the end of their discussions,” Mr Mitchell said. “We take this as a strong indicator of their belief that peace is possible.”
Nearly half a million Jews live in more than 100 settlements built since Israel’s 1967 occupation of the West Bank and East Jerusalem.
They are held to be illegal under international law, although Israel disputes this.
Mr Mitchell said Mrs Clinton would travel to Jordan later on Thursday for talks with Jordan’s King Abdullah II, while he meets Syrian President Bashar al-Assad in Damascus in an effort to revive Syrian-Israeli peace talks.
As the leaders held talks in Jerusalem, Palestinian militants fired a rocket at the southern port city of Ashkelon, along with several rounds of mortar fire along the Gaza-Israel border, the Israeli military said.
In response, the Israeli air force bombed Hamas tunnels in southern Gaza around midday on Wednesday, killing one Palestinian and wounding two.
It followed up with an overnight raid on two suspected weapons caches in the northern and southern Gaza Strip, the military said. Gaza’s governing Hamas movement said one of the sites hit was a soap factory.
The Popular Resistance Committees, a small militant group opposed to the talks, said it was behind the Palestinian militant attacks, which caused no casualties.
Although Hamas militants were not believed to have launched the attacks, Israeli officials accused the group of turning a blind eye to the activities of other factions in the territory that are opposed to the peace talks.
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