Morocco's King Hassan II has pledged to send 2,000 troops to join the 3,800-man multinational peace-keeping force already stationed in Lebanon, according to Lebanese reports.

The Moroccan commitment was sealed during talks between the monarch and Lebanese President Amin Gemayel, according to Lebanese journalists who accompanied Gemayel on his return to Beirut yesterday following a one-day trip to Rabat.

State Department officials said the Moroccan offer did not come as a surprise and that the United States would "try to be supportive" of Gemayel's efforts to expand the size and scope of the multinational contingents.

But in Jerusalem, a senior Israeli official said that Foreign Minister Yitzhak Shamir, meeting with U.S. special Mideast envoy Morris Draper, rejected the participation of Morocco and other countries that do not have "normal and friendly relations" with Israel, news agencies reported. Moroccan soldiers battled Israeli forces on the Golan Heights during the 1973 Arab-Israeli war.

Shamir was reported to have insisted to Draper that Israel would only agree to the positioning of peace-keeping soldiers in Lebanon who come from countries that maintain full diplomatic relations with Israel and are not regarded as enemies of the Jewish state, news agencies reported. Shamir said that Israel harbored no objections to Egyptian soldiers being sent to Lebanon on a peace-keeping mission, since Israel maintains diplomatic relations with Egypt.

Shamir stressed in his talks with Draper, though, that no other Arab countries could be considered at this time, according to the Israeli official.

While admitting that Israel's brusque refusal posed problems, a State Department official said there might be room for flexibility if Israeli security concerns were assuaged by locating Arab peace- keeping units in the northern and eastern parts of Lebanon.

Gemayel has traveled recently to European and Arab capitals soliciting troop contributions for a multinational peace-keeping force that he envisions could grow as large as 30,000.

So far, the Lebanese leader has not received any assurances from the U.S., French and Italian governments that the three Western countries are prepared to increase their troop commitments in Lebanon, but they have not formally turned down his request.

Britain has said it would seriously consider a formal request.

Lebanon has also contacted the Greek and Canadian governments about prospects of sending troops. So far, however, neither government has given a public response.

Besides the Moroccan forces, Gemayel is expected to request that peace-keeping contingents from Jordan and Saudi Arabia be dispatched in the near future, according to the privately owned Lebanese Central Information Agency.

Jordanian and Saudi forces would be sent to handle peace-keeping chores in the east and north while the U.S. Marines, French and Italian soldiers would help maintain stability in the capital, according to the Lebanese reports.

The 1,200-man U.S. force is expected to inaugurate today what President Reagan calls "limited" patrols in the eastern half of the capital, which remains under the control of private Christian militias.

Lebanese press reports said the expansion of the U.S. Marines' role was intended to prepare the area for deployment of the Lebanese Army in East Beirut and the possible disarming of the Christian militias.

The Arab peace-keeping contingents, if stationed in the eastern and northern parts of Lebanon, might provide a key security dimension to encourage Syrian President Hafez Assad to withdraw his country's 30,000 soldiers from the war-ravaged country.

Assad has repeatedly cited the security threat to his country if he pulled his forces out of Lebanon prior to withdrawal of Israel's estimated 70,000 troops now in Lebanon. Syrian forces are concentrated in the Bekaa Valley to protect what is widely considered the "soft" flank of Syria and the road to Damascus.

During his visit to Morocco, Gemayel reportedly gained a future commitment from King Hassan to increase his country's initial 2,000-man contribution once Israeli, Palestinian and Syrian forces have departed Lebanon.

In Jerusalem, Draper pressed ahead with Reagan administration efforts to insure the departure of all foreign occupation troops from Lebanon.

After briefing Shamir on his recent talks with Lebanese leaders, Draper told reporters: "I think we are making progress in overcoming the obstacles to talks aimed at bringing about the withdrawal of all foreign forces from Lebanon. That is the common objective of the U.S., Lebanon and Israel."

A senior Israeli government official indicated that the discussions so far have dealt more with the formalities of holding Israeli-Lebanese talks than with the specific proposals to get the foreign troops out of Lebanon.