Rabin and Arafat agreed to meet again in a week's time as officials tried to resolve these and other differences over extending Palestinian self-rule to the occupied West Bank.
Rabin sought to play down the notion of a crisis in the talks on implementing the long-stalled self-rule deal.
But Yasser Abed Rabbo, Arafat's aide in charge for information and culture, said: "I think there is a crisis, a real crisis. There are two tendencies and two approaches."
The two-hour meeting on the border between Israel and the Gaza Strip ended without an expected joint news conference. A stern-faced Arafat walked head down past reporters to his car to attend a meeting with a visiting European Union delegation headed by French Foreign Minister Alain Jupp?.
After that meeting in Gaza City, Arafat declined to comment on the talks with Rabin. Asked if the next meeting might break the stalemate, he said: "I am a pragmatic person. I am not dreaming."
Since the start of self-rule in Gaza and Jericho last May, the two sides have gone from meeting to meeting in Cairo, Gaza and elsewhere with little progress to report on the next stage, which includes Palestinian elections and Israeli troop redeployment.
An unprecedented four-way Arab-Israeli summit in Cairo last week was aimed at jump-starting talks. That meeting, labelled a "coalition for peace" by Israel's foreign minister, also broke up without an expected news conference.
Both Rabin and Arafat have staked their political futures on implementing their 17-month-old peace accord but have met obstacles at every step.
Support for the deal has eroded on both sides and Rabin's popularity has dipped since Islamic opponents of the accord began suicide-bomb attacks against Israelis last October.
Rabin said an 18-day-old ban on Palestinians entering Israel from the Gaza Strip and West Bank would remain in force. He imposed the closure after two Gaza suicide-bombers killed 21 Israelis in Israel last month.
Rabin said 2,000 more Palestinian policemen would be mobilized in self-rule areas to help security. He said Palestinians on Wednesday apparently prevented a man from carrying out a suicide attack in Israel. He did not elaborate.
Rabin told reporters, "There were differences but by no means will I describe this as a crisis.
"We decided, in the light of the fact that it wasn't possible from the standpoint of time and other circumstances to reach solutions today, to hold another discussion next week," he said.
Rabin said Arafat must take control of law enforcement. "From our standpoint the main dominant consideration is the matter of security," Rabin said.
In a further crackdown on militants Thursday, police raided a Gaza office of the Marxist Democratic Front for the Liberation of Palestine, which claimed responsibility for Monday's fatal shooting of an Israeli guard, Palestinian officials said.
A Message from The Moscow Times:
Dear readers,
We are facing unprecedented challenges. Russia's Prosecutor General's Office has designated The Moscow Times as an "undesirable" organization, criminalizing our work and putting our staff at risk of prosecution. This follows our earlier unjust labeling as a "foreign agent."
These actions are direct attempts to silence independent journalism in Russia. The authorities claim our work "discredits the decisions of the Russian leadership." We see things differently: we strive to provide accurate, unbiased reporting on Russia.
We, the journalists of The Moscow Times, refuse to be silenced. But to continue our work, we need your help.
Your support, no matter how small, makes a world of difference. If you can, please support us monthly starting from just $2. It's quick to set up, and every contribution makes a significant impact.
By supporting The Moscow Times, you're defending open, independent journalism in the face of repression. Thank you for standing with us.
Remind me later.