The Obama administration has made little headway in efforts to restart the talks, with the Palestinians refusing to sit down until Israel halts all settlement activity in the West Bank and east Jerusalem.
'Window of opportunity'
John Kerry, the chairman of the US Senate Foreign Relations Committee, told Al Jazeera that the "window of opportunity" for peace between Israel and the Palestinians is closing.
"It's closing becase of people's impatience, people's anger and frustrations, because of the situation in Gaza, because of Hezbollah and Hamas increasingly being armed, because of Iran, because of the anger people have about the continued sense of occupation," he said.
"I believe passionately that this is a critical moment for dealing with the issue of Israel, Palestine and peace."
Clinton was also scheduled to meet Sheikh Hamad bin Jassim al-Thani, Qatar's prime minister, as well as Recep Tayyip Erdogan, the Turkish prime minister, on the sidelines of the forum, which is jointly organised by the Qatari foreign ministry and the US Brookings Institution.
She is to hold talks with King Abdullah of Saudi Arabia on Monday.
Iranian nuclear programme
Her visit comes as the US continues with a push to persuade Iran to rein in a nuclear programme which the West, as well as many Arab states, believes could be a cover an atomic weapons programme.
The US is making efforts to enlist the UN Security Council to impose a fourth round of sanctions on Iran, which says its nuclear programme is to simply to meet its civilian needs.
"We believe that all countries have a part to play in helping to sharpen the question for Iran"
US assistant secretary of state
US officials hinted that Saudi Arabia could help in that effort diplomatically by offering Beijing guarantees it would meet Chinese oil requirements, a step that might ease Beijing's reluctance to impose further sanctions on Iran.
China, which wields a veto on the Security Council, has lucrative commercial relationships with Iran and, along with Russia, has worked to dilute previous sanctions resolutions.
"We believe that all countries have a part to play in helping to sharpen the question for Iran," Jeffrey Feltman, the US assistant secretary of state, said.
"We would expect them [the Saudis] to use these visits, to use their relationships, in ways that can help increase the pressure that Iran would feel," he added.
Other US officials, who spoke on condition they not be identified, said they believed Saudi Arabia had made some gestures towards China on fuel assurances but gave no details.
"There have been some recent, positive moves," said one official, without elaborating.
Meanwhile, Erdogan, in remarks earlier on Sunday, said Turkey is willing to serve as the venue for an exchange of Iranian nuclear fuel in a potential settlement between the West and Iran.
"The International Atomic Energy Agency has said Turkey could serve as the centre for the exchange of uranium ... but there is no agreement up until now," he said.
"If Turkey is chosen, it will do what it is asked to do."