Middle East envoy George Mitchell wound up a second round of indirect peace talks between Palestinians and Israeli without any outward sign of progress.
A statement from the office of the Israeli PM Benjamin Netanyahu spoke of the "possibility" of goodwill gestures towards the Palestinians. No details were given.
The US envoy and Mr Netanyahu met for three and a half hours on Thursday. Mr Mitchell met Palestinian leader Mahmoud Abbas earlier in the week.
The indirect, proximity talks are set to continue for four months, and should get to addressing some of the core issues - borders, Jerusalem, and refugees.
All parties say they hope these will lead to direct negotiations.
In the current talks Mr Mitchell shuttles between Mr Netanyahu's office in Jerusalem and Mr Abbas' office in Ramallah, a journey of about 10 miles (15km).
Thursday's statement from Mr Netanyahu's office said part of the meeting with Mr Mitchell concentrated on water issues.
The US envoy met Mr Abbas on Wednesday. He was given letters protesting against the killing of a Palestinian teenager in the West Bank, allegedly by an Israeli settler, and the killing of an elderly farmer in Gaza by the Israeli military.
Palestinian chief negotiator Saeb Erekat said his side also brought up the "the numerous Israeli provocative statements of the last few days".
Palestinian officials have been angered by repeated statements by Israeli officials, including the prime minister, that settlement construction would continue in occupied East Jerusalem.
The Palestinian Islamist group, Hamas, which controls the Gaza Strip, has criticised the talks, warning that they "give cover to the Israeli occupation to commit more crimes against our people".
The proximity talks were meant to start in March, but Palestinians pulled out of talks after Israeli municipal authorities approved plans for 1,600 new homes in the East Jerusalem settlement of Ramat Shlomo.
The announcement was made during a visit to Israel by US Vice-President Joe Biden and caused great strain in Israeli-US relations.
The Palestinian Authority's formal position is that it will not enter direct talks unless Israel completely halts building in the West Bank and East Jerusalem.
In November, Israel announced a 10-month suspension of new building in the West Bank, under intense US pressure.
But it considers areas within the Jerusalem municipality as its territory and thus not subject to the restrictions.
Israel has occupied the West Bank, including East Jerusalem, since 1967. It insists Jerusalem will remain its undivided capital, although Palestinians want to establish their capital in the east of the city, and the international community does not recognise the Israeli annexation of the east of the city.
Nearly half a million Jews live in more than 100 settlements in the West Bank, among a Palestinian population of about 2.5 million.
The settlements are illegal under international law, although Israel disputes this.