Israel's government expressed coolness yesterday toward President Carter's reported readliness to offer deployment of U.S. troops on the West Bank and Gaza Strip, saying that the Israeli Army must remain the "center pillar" of security in the occupied territories after any peace agreement.

The response followed reports in Washington that Carter is prepared to propose placing U.S. air defense in the Sinai Peninsula and U.S. peace-keeping forces in the West Bank if these proposals are needed to break a Camp David summit deadlock. Foreign Ministry officials said airbase in the Sinai are a "very viable possibility" but that American troops in the occupied West Bank could not be a substitute for Israeli military presence there.

Israeli defense forces, a ministry spokesman said, could "be padded with all sorts of deployments" but he added, "the main center pillar must be Israeli personnel."

Proposals to U.S. forces to guarantee a Middle East settlement have surfaced previously during the Carter administration. The reports indicated that the idea was being considered again, this time for presentation at Camp David.

Carter said yesterday in Idaho that he was "reluctant" to use U.S. troops to guarantee a Middle East settlement, but indicated that the option would stay open for discussion at the summit. (Details on Page A7).

Israeli Foreign Minister Moshe Dayan had expressed similar reservations in response to reports that U.S. National Security Adviser Zbigniew Brzezinzki favored an increased U.S. military role in the Middle East under a regional security agreement.

The Foreign Ministry spokesman noted that the possibility of a U.S. military presence in the Sinai, including air bases, was implict in Israel's peace proposals.

"But if we are talking about the West Bank, it can only be as an addition and not as a substitute for the deployment of Israeli military personnel," the spokesman said.

Topographical differences between the vast Sinai and the relatively compact West Bank, he said, account for the contrast in Israel's attitude toward the two regions.In response to a question, he said that was the only difference that influenced Israel's position on the issue.

Under Israel's peace plan, the Sinai would be demilitarized for the most part, and any military movements could be detected by aerial surveilance and electronic monitoring systems, he noted. However, in the West Bank, he said, "before you turn left or right, somebody bites your ear."

Since any U.S. offer at Camp David to deploy troops in the West Bank and Gaza presumably would be made to soften Egyptian President Anwar Sadat's opposition to any continued Israeli Army presence in the area, Israel's current posture on the issue suggests little room for agreement without a major shift by one side or the other.

Egypt's six-point peace plan calls for immediate withdrawl of the Israeli Army from the occupied territories, as well as a withdrawal of Jewish settlers.

Following a meeting last month in Salzburg, Austria, with Israeli Defense Minister Ezer Weizman, Sadat was reported to have told Weizman that Israel would be able to maintain some military presence on the West Bank as defined by Israel's security needs.

The Egyptian government has since denied, however, that Sadat made such an offer, and it reiterated Egypt's longstanding opposition to having any Israeli troops in the areas.

Israel's coolness to a dominant U.S. peacekeeping role in the territories parallels a similar attitude to reported designs by French President Valery Giscard d'Estaing to increase French influence in a Middle East peace settlement by offering French troops for West Bank peacekeeping duties under U.N. auspices.

Sadat plans to stop over in Paris on his way to Camp David and meet with the French president, who reportedly is prepared to raise his proposals publicly if the summit meeting results in continued stalemate. Western diplomatic sources said Frence has already made its proposals known privately through diplomatic channels.

Israeli officials are known to have reacted to these suggestions with the same reservations concerning Israeli predominance in any post-agreement security force in the West Bank and Gaza.

Meanwhile, Israel yesterday formally warned both the United States and the United Nations of what officials termed a "worsening" situation in Lebanon, where Christian Phalangist and National Liberal Party militias are still under attack by the Syrian Army.

Prime Minister Menachem Begin summoned U.S. Embassy Charge d'Affairs Samuel Hart to a meeting at which the prime minister reportedly warned the U.S. envoy of the "gravity" of the situation and asked the Carter administration to influence Damascus to control the Syrian army.

Syria, according to reports from Damascus, previously had warned Israel against intervening in Beruit and the northern mountain area where the Christian militias are under assault.

The State-Department has said that it is in touch with all the parties in the dispute, including Syria.

Apart from some veiled warnings of intervention made on Monday by two Israel legislators, which the Israeli government did nothing to dispel, government officials have said little, apparently in response to U.S. pleas for moderation.

Two approaches are being debated among government officials here. One holds that the Lebanon crisis - as serious as it is - must be secondary to Camp David, and that all efforts at influencing the Syrians must be made through diplomatic channels.

Advocates of a hard line argue that Israel should inform Syria firmly of a line beyond which it will tolerate no further Syrian Army offensive, and then, if necessary, send Israeli war-planes to support the Christian ground forces.