Israeli and Palestinian leaders have made progress on the issue of Jewish West Bank settlements in the latest round of Middle East peace talks, US envoy George Mitchell has said.
His comments came after the two sides continued direct talks in Jerusalem.
The Palestinians say they will walk out of the talks if a partial Israeli ban on settlement building is not extended.
Israel has so far refused to renew the restrictions, which are due to expire on 26 September.
The talks resumed two weeks ago, after a 20-month gap.
"I will say that 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."
Palestinian President Mahmoud Abbas met Israeli Prime Minister Benjamin Netanyahu at his official residence in Jerusalem in talks mediated by the US Secretary of State, Hillary Clinton.
The talks were a continuation of negotiations which began in the Egyptian resort of Sharm-el-Sheikh on Tuesday.
Few details of substance have emerged.
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.
President Abbas's spokesman, Nabil Abu Rudeina, described the talks as "serious and deep, but the obstacle of settlements still exists".
Mr Netanyahu's spokesman said both sides had to make hard decisions.
"The way to an agreement is to look at all the core issues together, not to run away from any one of them," Mark Regev told the Associated Press news agency.
"If the expectation is that only Israel has to show flexibility, then that is not a prescription for a successful process."
Mr Mitchell said the talks in Jerusalem would be followed by lower-level discussions between Israeli and Palestinian negotiating teams in the coming days.
Status of Jerusalem
On Sunday, Mr Netanyahu said he could not extend the current ban on West Bank settlement construction - but nonetheless would not allow thousands of planned homes to be built.
US officials said two concessions which Mr Abbas could make were recognising Israel as the Jewish homeland, something the Palestinians have so far resisted, and agreeing quickly to the final borders of a future Palestinian state.
The status of Jerusalem is itself one of the most divisive issues. Israel claims the city as its eternal, undivided capital, while the Palestinians want East Jerusalem to be the capital of any future Palestinian state.
Another problem facing negotiators is that only one part of the Palestinian territories is represented because the Islamist movement Hamas, which controls the Gaza Strip, opposes the talks.
A senior Hamas leader in Gaza, Mahmoud Zahhar, told the BBC the movement would not attempt to stop the talks because they would "reach an end, as previous ones" by themselves.
Last week, four Jewish settlers were killed when their car came under fire near the West Bank city of Hebron. Hamas said it was behind the attack.
Hours before Wednesday's trilateral meeting, Israeli aircraft bombed tunnels used by smugglers under Gaza's border with Egypt, killing one Palestinian.
The raids came shortly after militants in Gaza fired several rockets and mortars into southern Israel. There were no reports of any casualties.