The Arab powers today imposed strict new curbs on Palestinian political and military activities in Lebanon as part of their campaign to bring a tamed Palestinian force to the Middle East peace talks.

The new rules take away the last bastion where the Palestinians have military and political freedom of action. Since they were thrown out of Jordan six years ago, Beirut has became the heart of the Palestinian movement - the headquarters of all major Palestinian leaders and their groups.

Regulations agreed on today by the four-power committee named by the Arab states to supervise the peace in Lebanon would take away the Palestinians' right to keep arms in their camps, restrict their guerrilla presence to a still-unspecified area near the Isreali border and make them financially liable for any damage suffered by a Lebanese from Israeli raids mounted in retaliation against Palestinian activities.

Politically, the freedom of speech of Palestinian leaders within Lebanon will be curbed and, ad a further blow for their prestige in the Arab world, Palestinian leaders will be forbidden to have more than two armed body-guards instead of the dozen or so many of them now travel with.

This is the first formal acknowledgement of the Arab powers four-month policy of taming the Palestinians politically and militarily.

The process of bringing the Palestinians to heel in their camps around Beirut has already begun, said Egypt's ambassador, Ahmad Lutfi Mitwalli, a member of the four-power committee along with the representatives of Syria, Saudi Arabia and Kuwait.

Fierce clashes between Palestinian fighters and Syrian troops of the Arab peacekeeping force in the camps Thursday and yesterday signaled the beginning of that process.

Informed sources have reported today that over the past two days the Syrians had arrested at least 60 members of extremist "Rejection Front" Palestinian groups - those who oppose any settlement that allows for Israel's continued existence. In addition, the Syrians reportedly collected truckloads of arms and ammunition from the Palestinian camps.

"The next week will be the week of raids," said Saudi Ambassador Ali Shaer.

Palestinian sources have remained quiet on the new Arab moves. They have known about the rules for weeks and have tried to fight them politically.

Yasser Arafat, leader of the Palestinian Liberation Organization, was in Cairo today talking with Egyptian officials. Some sources here said he oppose the new restrictions and was appealing to Arab laders to change their minds, while other sources said he secretly favors restrictions - especially on the "Rejection Front."

The new Arab move comes just before Secretary of State Cyrus R. Vance's fact-finding tour to the region, which is to begin Monday. The Arab leaders are anxious to convince Vance - and through him the Israelis - of their new moderate stance and their strong desire for a peace settlement.

Rules applied to the Palestinians here in the past rarely were enforced with vigor. It remains to be seen if the new restrictions will be more rigidly applied. Their exact wording was not released by the four-power committee, but the Associated Press here obtained a copy that was verified by two sources.

The new rules supplant the 1969 Cairo agreement, which allowed the Palestinians to maintain a military and political presence in Lebanon that at times verged on being a state within a state.

The presence was one of the causes of the 19-month civil war here, as largely Christians rightists objected to Palestinians' carrying weapons in the streets of Beirut and manning roadblocks and checkpoints near their camps. The new curbs will go a long way toward meeting the rightists' objections.

Under the new policy, all heavy weapons - tanks, machine guns, artillery pieces and mortars - are banned from the 15 Palestinian camps in Lebanon, and only the Palestinians allowed to have weapons are the police force known as the Palestinian Armed Struggle Command. They are restricted to automatic rifles, called "personal weapons" in this gun-happy country. Moreover, the rules allowed only five police for every 1,000 camp residents.

This means the Palestinians would be outgunned by their Lebanese neighbors, since it is the custom here for every house to have at least one weapon - most often an automatic rifle.

All heavy weapons and Palestinian fighters must leave the camps and go to still-undesignated sites in southern Lebanon. Heavy clashes between Palestinians and Lebanese rightists were reported in that area today.

The new rules limit the number of Palestinians refugees allowed in the country to 200,000 - about 150,000 fewer than are currently living in Lebanon. The 200,000 figure is the number of Palestinian refugees registered with the United Nations in 1969.

Palestinian propaganda activities here will also be greatly restricted by the new regulations. Their radio stations will be banned and all Palestinians will be subject to Lebanese press laws, which include paying a $250,000 franchise tax. Palestinian officials are forbidden to take part in any Lebanese political activities.

In other Middle East developments:

Israeli officials reported that Syrian forces have begun withdrawing from southern Lebanon. Military officials said, however, that three bazooka shells were fired from Lebanese territory at an Israel patrol in northern Galilee Friday night, the first such incident in that area in more than a year.

Arab youths stoned vehicles in the occupied West Bank town of the Nablus.

Egyptian university students, defying a new security law, staged anti-government demonstrations in Cairo.