Clinton, standing alongside Israeli Prime Minister Benjamin Netanyahu, said they had engaged in "extensive discussions" about Syria and the peace process. But Clinton declined to reveal any details when asked if they had discussed any new Israeli proposals for land concessions in the Golan Heights.
Clinton said talking publicly of any such proposals would set back negotiations. But he added: "I do feel encouraged by the discussions we have had that there are things worth working on."
Netanyahu, for his part, said Syria could show its good faith by exerting its influence in Lebanon to reduce the military capacity of Hezbollah terrorists.
Until then, he said Israel would not withdraw its troops from southern Lebanon because "if we simply walked away ... Hezbollah and other terrorists would simply come to the (border) and attack our towns and villages."
It was Clinton's first meeting with Netanyahu since the Israeli leader and Palestinian Chief Yasser Arafat ended a dangerous impasse last month by agreeing to, then implementing, Israel's long-delayed pullout from Hebron and parts of the West Bank.
Referring to the Hebron agreement, Clinton said: "There is a renewed sense of promise in the Middle East."
Netanyahu said Israel already has acted and the next moves should come from others. "I think we've taken bold steps for peace," the Israeli leader said.
"It's time that we see such steps from our partners as well," the prime minister said. "And if we have this mutuality, we will have, I think, a great future, a different future and hope for our children and our grandchildren."
Netanyahu was the first of four Middle East leaders scheduled to meet Clinton in coming weeks. The president also will see Arafat, Egyptian President Hosni Mubarak and Jordan's King Hussein.
In talks with Netanyahu, Clinton explored possible steps toward resuming peace talks with Syria. Those discussions were broken off a year ago after Islamic militants carried out suicide bombings in Israel.
Syria is insisting that Israel surrender the Golan Heights, a strategic plateau along their border, as its price for peace. Israel captured the Golan in the 1967 Six-Day War.
Netanyahu was said to have brought to Washington a territorial compromise on the Golan. The United States believes Syrian President Hafez Assad will not sign a peace agreement without getting back all of the plateau.
In the Hebron agreement, Netanyahu accepted the principle of pulling Israeli troops back from land claimed by the Arabs. Previous Israeli governments had supported the land-for-peace formula favored by the Arabs and the United States, and were said even to have promised Syria to leave the Golan, but Netanyahu had been a holdout until last month's agreement.