The two leaders held three hours of discussions in Washington on the latest US proposals for peace with Israel.
Mr Clinton, who leaves office on 20 January, is expected to speak to the Israeli Prime Minister, Ehud Barak, by phone later on Wednesday.
Mr Arafat is due to meet Arab foreign ministers later in the week - after that his formal response to the Clinton plan is expected.
Clarifications
During their talks, Mr Clinton sought to answer Mr Arafat's questions about the framework plan.
The White House spokesman, Jake Siewert, said Mr Arafat told Mr Clinton that he "is prepared to immediately resume co-operation on terrorism, to intensify efforts to stop the shootings, and to arrest those responsible for the violence".
Mr Siewert said a peace deal on sensitive political issues would be difficult "while there is an atmosphere of violence, and I think everyone understands that".
More than 350 people, mostly Palestinians, have been killed since the Palestinians launched their uprising three months ago.
While the talks went on, Israeli tanks exchanged fire with Palestinian police near the West Bank town of Ramallah. One policeman was wounded.
Israel radio said the Israeli army closed major roads in the Gaza Strip on Wednesday, cutting the territory into three parts.
It said Palestinian forces fired at the Netzarim Jewish settlement overnight, but there were no reports of casualties.
Doubts on both sides
Mr Barak has said he does not believe Mr Clinton can broker a peace agreement before his presidential term ends.
Mr Arafat's concerns over the Clinton plan centred on three issues.
He says the plan
One issue raised by Mr Arafat was sovereignty over the area in the Old City of Jerusalem known to Arabs as the Noble Sanctuary, and to the Jews as the Temple Mount. This contains the Al-Aqsa mosque, a vital objective for the Palestinians.
Mr Clinton proposes that the Palestinians have sovereignty over the disputed area's surface, with the Israelis in charge of the supporting Western Wall, a centre for Jewish prayer. Neither side would be able to engage in archeological excavations there. Mr Arafat wanted to find out exactly how this would work.
Mr Barak said he would consider sending representatives to Washington if there was a halt to "terrorism" and a resumption of Israeli-Palestinian security co-operation.
He has said he will not sign any accord giving the Palestinians complete sovereignty over the Al-Aqsa mosque compound.