Secretary of State Edmund S. Muskie, concerned about the mounting violence on the Israeli-occupied West Bank, appealed yesterday "to both Arabs and Israelis to exercise maximum restraint" and avoid the further use of terrorism.

In a statement read for him by State Department spokesman Hodding Carter, Muskie said: "Terrorism is unacceptable for any reason by any party."

Referring to the U.S.-mediated effort by Egypt and Israel to negotiate a limited self-government system for the Palestinian inhabitants of the West Bank and Gaza Strip, Muskie added:

"Onced begun, the cycle of violence can only lead us away from our fundamental goals. This is a time for cooling down of emotions and for reason to prevail over passion."

Six Jewish settlers were killed last month during an Arab terrorist ambush in the West Bank city of Hebron, and there has now been a series of incidents this week, including car bombings in which two Palestinian mayors were seriously injured.

In addition, Palestine Liberation Organization leader Yasser Arafat's Fateh group, largest of the guerrilla factions under the PLO umbrella, has vowed to begin a new campaign of terrorism against Israel. In apparent response, Israel staged heavy attacks Wednesday night against PLO forces in southern Lebanon.

This sharp upsurge of violence and bellicose rhetoric has caused increasing concern in U.S. official circles that if passions remain unchecked, there could be long and potentially serious delays in getting the stalled autonomy talks going again and persuading Palestinian inhabitants of the occupied territories to cooperate with the peace process.

In addition to intensive behind-the-scenes efforts by President Carter's Mideast negotiator, Sol M. Linowitz, to revive the talks, Muskie is known to be considering making a major policy speech outlining some new U.S. proposals on peace in the Middle East.

Reliable sources said yesterday that drafts of the speech are still being worked on inside the State Department, but they added that a decision has not been made about when or even if Muskie will deliver the speech.

In a related move yesterday, the State Department took the symbolically important step of granting a high-level audience to two West Bank Palestinian mayors who were deported last month after Israeli military authorities accused them of inciting terrorism.

The two, Fahd Kawasme of Hebron and Mohammed Milhem of Halhoul, together with a religious leader, Sheik Rajab Tamini of Hebron, met with U.S. officials including Harold Saunders, assistant secretary for Middle East affairs, and Robert Hunter of the White House National Security Council staff.

The two mayors have said that only the PLO can represent West Bank Palestinians. State Department officials said the decision to receive them does not imply any breach of the Carter administration's refusal to engage in direct contacts with the PLO.

The officials said they were being received as influential West Bank residents whom the United States believes should be allowed to return to their homes. Asked if their return would ease tensions on the West Bank, Hodding Carter replied:

"The more nearly normal a situation that can be created on the West Bank, the more nearly able the parties are going to be to work out the accommodation which must be found . . ."

In what seemed almost like an attempt to balance the meeting with the mayors, Teddy Kollek, the Israeli mayor of Jerusalem, was honored yesterday at a White House luncheon given by Vice President Mondale and attended by Muskie. President Carter also made a brief appearance at the end of the luncheon and, in a gesture to Israeli sentiment, reiterated U.S. opposition to any moves to redivide Jerusalem.

The two mayors, who are visiting the United States to try to rally support for their efforts to return home, became the focus of local controversy Wednesday night when they appeared at an open meeting at Temple Sinai in Northwest Washington. Their "dialogue" almost turned into an open battle between Jewish supporters of hard and soft lines on the Palestinian issue.

At a luncheon with reporters yesterday, the two rejected the idea of Palestinian cooperation with the autonomy talks and insisted that any Palestinian solution must include Israeli withdrawal from the occupied territories and recognition of the right to form an independent Palestinian state under PLO leadership.

Avi Pazner, press spokesman of the Israeli embassy, said later that the two mayors, by their statements yesterday, had endorsed the Fateh position that Israel must be "liquidated" and added that "no credence should be given to the lies that they came here to disseminate."