Reverberations from the new U.S.-Israeli strategic cooperation agreement echoed through the Middle East today, further complicating the U.S. peace-making role in the region and causing the Israeli government to scramble to ward off defeat in parliament.

As U.S. special envoy Philip Habib reportedly was told by a key Syrian official that the accord disqualified Washington from acting as a mediator in the Middle East, Israeli Prime Minister Menachem Begin's coalition government faced four no-confidence motions in parliament introduced by opposition parties criticizing the agreement with the United States.

Israeli Defense Minister Ariel Sharon, who signed the strategic cooperation accord in Washington Monday, rushed home to take part in the vote, expected Wednesday at the earliest. Three other Israeli Cabinet members also were recalled to help the government win the required 61 votes in the 120-member parliament.

Begin, who is recovering from surgery on a broken thighbone, will not be able to attend the parliamentary debate, but his absence will be offset by Labor Party Secretary-General Haim Barlev, who is also recuperating from surgery, according to wire service reports quoting parliamentary sources.

The sources said that if all ministers return home on time, the coalition will ride out the no-confidence vote without difficulty.

The U.S.-Israeli accord, called a memorandum of understanding on strategic cooperation, provides for joint naval and air exercises in the eastern Mediterranean, joint planning, exchange of military assistance and the establishment of a coordinating council between the two nations.

Sharon, who initially sought a more explicit and wider-ranging strategic cooperation agreement described what he got as not "everything we wanted but . . . most of what we wanted." He called the accord a "turning point" in U.S.-Israeli relations and predicted Knesset (parliament) passage.

The four no-confidence motions were being introduced by parties as far apart politically as the left-of-center Labor Party, the right-wing Tehiya (Revival) Party, the middle-of-the road Shinui (Change) Party and the Communist Hadash front.

Yitzhak Rabin, of the Labor Party, said the memorandum was hastily signed, and unnecessary in the first place.

The purpose of the accord is to combat military threats from the Soviet Union or its surrogates in the Middle East. U.S. officials emphasized Monday that it is in no way directed against Arab nations.

However, several Arab states, including Syria, Kuwait and Libya, as well as the Palestine Liberation Organization, described the accord as precisely that: an anti-Arab alliance.

The purpose of Habib's visit was to shore up a tenuous cease-fire he helped coordinate last summer between the Israelis and Palestinian guerrillas in southern Lebanon and to discuss Israel's demand for the removal of Syrian anti-aircraft missiles from Lebanon's eastern Bekaa Valley.

But the U.S. envoy's efforts were overshadowed by reportedly hostile reaction from Syrian officials to the U.S.-Israeli agreement.

Syrian Foreign Minister Abdul Halim Khaddam told Habib, "the United States has no longer the right to play any mediation or arbitration role in the Arab-Israeli conflict because you have become a direct party in this conflict," according to Syrian sources quoted by Associated Press.

The sources declined to be identified, but in a country where the media is as tightly controlled as in Syria, information about events in the government leaked to foreign wire services usually has the government's blessing.

Khaddam reportedly told Habib: "Since your last visit here, nothing has changed in the area except that Israel is becoming more aggressive in deeds and threats." And now, he added, the U.S. government has "signed an agreement of strategic alliance with Israel."

Officially, the Syrian government made no immediate comment on the signing of the agreement but it reportedly has urged the Soviet Union to conclude a similar agreement with the Arabs.

Syria has had a treaty of friendship and cooperation with the Soviet Union for 20 years.

Habib drove from Beirut, where he had two days of talks with Lebanese leaders, by motorcade to Damascus via the Bekaa Valley and within half a mile of the missile positions.

It is the U.S. envoy's fourth Mideast tour since last spring, when he first tried to defuse the missile issue. Syria installed the Soviet-made SA6 and SA2 missiles after Israeli planes downed two Syrian helicopters in the Bekaa last April, saying their purpose was to defend Syrian peace-keeping forces in Lebanon.

Israel recently has renewed threats of military action if Habib cannot get Syria to withdraw the missiles.

Syria stationed forces in Lebanon to end continuous fighting between Lebanese Christian forces backed by Israel and the Palestine Liberation Organization and its factions.

The PLO had the strongest words of criticism yesterday for the U.S-Israeli agreement.

Yasser Abed Rabbo, a member of the PLO executive committee, described the accord as a "declaration of American-Israeli war against the Arabs."

He urged a meeting of Arab hard-liners, as well as those Arab states that rejected the Saudi peace proposal at the recent Arab summit in Fez, Morocco, to coordinate opposition to the U.S.-Israeli agreement. He added, the memorandum "shows how superficial are the attitudes of those states which preach settlements in the region, such as the Saudi plan, through the role of the United States."

There was no immediate reaction from Saudi Arabia, but the kingdom had criticized the idea, when it first became known last September, as an obstacle to the Middle East peace process.

In Moscow, the official Tass news agency characterized the accord as "a new aggressive military strategic allicance" spearheaded in the first place against the Arab countries.