Palestinian president Mahmoud Abbas said he is hopeful after his first meeting with US president Donald Trump, although they did not discuss the specifics of restarting Israeli-Palestinian negotiations.
Mr Abbas said he believes the Trump administration can play an important role as a mediator.
"What is needed is to bring the two parties together, to bring them closer and then to facilitate things between them," he said after the White House meeting.
Mr Trump also struck an optimistic note, saying he believes an Israeli-Palestinian deal can be reached.
The Palestinians want to set up a state in the West Bank, Gaza Strip and east Jerusalem, lands Israel captured in the 1967 Middle East war. Mr Abbas reiterated the demand as he stood next to Mr Trump.
There have been no serious negotiations since gaps widened with the 2009 election of Benjamin Netanyahu as Israel's prime minister.
Mr Netanyahu rejects the 1967 frontier as a baseline for border talks and rules out a partition of Jerusalem where Palestinians hope to establish a capital.
The Netanyahu government, like those before it, has expanded settlements on war-won lands, despite US appeals to curb construction.
Mr Abbas described his meeting with Mr Trump as positive and said "we build hopes on it".
"So far, we didn't talk about a mechanism, but the contacts between us and the Americans began and will continue," he said.
Mr Abbas said he is ready to meet Mr Netanyahu, and suggested the Israeli leader is avoiding such talks.
"We had planned to meet in Moscow, but he didn't show up," Mr Abbas said, referring to Russian efforts several months ago to set up talks.
Mr Netanyahu has said he is willing to meet Mr Abbas.
In the past, Mr Abbas balked at the idea of such a summit, saying it would be pointless without general agreement on the framework of negotiations and a significant curb in settlement construction.
On Thursday, Mr Netanyahu said he looks forward to discussing with Mr Trump the "best ways to advance peace". Mr Trump is reportedly visiting Israel at the end of the month.
He said Mr Abbas's comments that Palestinians are cultivating a culture of peace "are unfortunately not true", pointing to Palestinian schools named after militants who killed Israelis.
"But I hope that it's possible to achieve a change and to pursue a genuine peace. This is something Israel is always ready for.", Mr Netanyahu said.
US officials had said Mr Trump would press Mr Abbas to end payments to families of Palestinians in Israeli jails.
A senior US official said on Tuesday that the issue of payments had been raised in preliminary talks with the Palestinians in Washington.
Mr Abbas said the issue was not raised in his talks with Mr Trump. Officials said it would be addressed in a future meeting.
His positive portrayal of the meeting with Mr Trump may not be enough for a sceptical public at home.
Many Palestinians have become disillusioned with Mr Abbas' strategy, after two decades of intermittent US-led negotiations ended in failure while Israeli settlements keep expanding.
In the West Bank, the main focus appears to be a hunger strike by hundreds of Palestinian prisoners held by Israel, now in its 18th day.
Mr Abbas also faces fierce opposition from his main political rival, the Islamic militant group Hamas. It has dismissed Mr Abbas' strategy of negotiations and said he does not represent Palestinians.
After a decade of failed reconciliation attempts, Mr Abbas recently adopted a tougher stance toward Hamas, saying he would use financial pressure to force the militants to cede ground.