Clinton said "there was some progress made" in his talks with the Syrian leader and American officials appeared to be encouraged by evidence that Assad was showing new flexibility on conditions for peace with Israel.
Landing in Tel Aviv, the fourth stop of his six-nation tour, Clinton described his relationship with the Syrian leader as "businesslike."
"We don't call each other by our first names," said Clinton. "We have developed a relationship where at least to this point, neither has reason to question the other's credibility. He's a tough man."
Assad, speaking after the two leaders met in the presidential palace in Damascus, said Syria wanted "full withdrawal for full peace," adding that Israel must return to Syria the Golan Heights it seized in the 1967 war as well as returning land it seized in southern Lebanon.
Clinton conceded that getting a peace agreement with Syria remains "a key to achieving a comprehensive peace" in the region.
"Our job will not be done and we will not rest until peace agreements between Israel and Syria and Israel and Lebanon are reached," Clinton declared.
A day after he witnessed the historic signing of a peace agreement between Jordan and Israel, he pressed Assad to move forward on stalled peace talks with Israel. With Wednesday's accord, Syria and Lebanon remain the last two Arab states on Israel's border still officially at war with the Jewish state.
Clinton, the first U.S. president to visit Syria since Richard Nixon in 1974, said that he believed Assad was "committed to achieving peace."
Secretary of State Warren Christopher, talking to reporters en route to Tel Aviv aboard Air Force One, said that Clinton and Assad had "made substantive progress on more than one issue. That, I regard as being important." He declined to cite specifics.
Clinton had hoped to bring a new Syrian offer to Israel. But Assad's assertion that it would not deal unless Israel returned the land it seized fell short of a major new Syrian overture. Clinton said Assad's statement had "gone beyond" previous Syrian positions.
He said he would discuss the talks in Jerusalem with Israeli Prime Minister Yitzhak Rabin, adding that there were some things he and Assad had talked about which he could not disclose publicly.
Asked if he was frustated about the continuing disagreement between Syria and Israel over the disposition of the Arab lands, Clinton said: "I wish we were signing a peace treaty on this trip. We won't do it."
Syria remains on the State Department's list of countries that support terrorism.
At the news conference, Assad rejected the accusation that Syria sponsored terrorism. "In any rate this was not one of the topics on the agenda in my discussions with President Clinton," the Syrian leader said.
But Clinton said: "We do not, we can not and we will not support the killing of innocent civilians. President Assad said to me that he thought that was wrong wherever it occured."
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