Syria and its Druze allies were guarded today in their initial responses to President Reagan's decision to authorize U.S. commanders in Lebanon to use air strikes and artillery fire to help the Lebanese Army and U.S. marines here.

There was relative calm today in the Chouf mountains overlooking Beirut, scene of 10 days of ground and artillery battles, but the indications were that neither Syria nor the Druze had decided what course to take next.

Tonight, Lebanese Foreign Minister Elie Salem, in a televised address, sought to reassure Syria that Lebanon's appeals for U.S. intervention in the conflict did not mean it wanted to engage the United States in a war with Syria.

Striking a conciliatory tone, Salem also said Lebanon is still willing to negotiate political, economic and security issues in exchange for the withdrawal of Syrian forces but he said Lebanon felt compelled to stick by its May 17 agreement with Israel and would accede to Syria's demand that it be canceled only if Syria came up with another plan to get Israel to withdraw.

France sought to distance itself from the escalation of the American role here and stressed that its troops in the multinational peace-keeping force here were not in need of U.S. help.

"Our forces in the region are capable of assuring their own protection," said a statement released by the French Embassy in Washington today.

The French are known to feel that the wider U.S. role seriously risks involving the United States in the internal conflict here. They appear to fear that U.S. bolstering of the Christian-dominated government of President Amin Gemayel will hinder efforts to frame a coalition government.

Robert C. McFarlane, Reagan's special Middle East envoy, flew to Damascus this afternoon where he met for 90 minutes with Syrian Foreign Minister Abdel Halim Khaddam in apparent continuous efforts to arrange a cease-fire in the fighting in Lebanon.

McFarlane also conferred briefly there with Saudi Arabian mediator Prince Bandar bin Sultan amid numerous rumors that the Saudis felt Reagan's new order complicated the cease-fire negotiations.

There were unconfirmed reports that the Saudis had asked the United States to hold off for 48 hours before taking any new military action.

Ghassam Tueni, a top adviser to Gemayel, said in Washington that Lebanon is considering a Saudi plan in which observers from Saudi Arabia and Syria would oversee efforts to reconcile the rival factions in Lebanon. Tueni said the plan called for a cease-fire in the Chouf mountains and a "national dialogue" among the many feuding groups.

The response of the Syrians to Reagan today was to charge that the United States was stepping into a quagmire in Lebanon as it had done in Vietnam.

The Syrian government newspaper Tishrin said this morning: "The bay of Beirut is the Gulf of Tonkin. Amin Gemayel is Nguyen Cao Ky. The humiliation in Vietnam will be repeated in Lebanon."

A spokesman for the Druze Progressive Socialist Party militia, which has been backed by Syria in its drive to force the Phalangist militia and the Lebanese Army out of the Chouf, said they were not concerned about the threat of Reagan's new instructions.

The new policy came amid deep concern here that the Druze and their allies would soon capture Suq al Gharb, a Chouf mountain stronghold handed over to the Lebanese Army early last week by retreating Christian Phalangists.

The town, on strategic heights above the presidential palace, has been attacked each of the past four nights. In the fiercest assault Saturday, most of a Lebanese Army company was killed, wounded or taken prisoner.

Americans feared that the fall of Suq al Gharb would make the frail government of Gemayel extremely vulnerable and the decision to widen the U.S. role was made after an appeal by Gemayel to Secretary of State George P. Shultz.

Lebanese officials indicated this week that they want the United States to use its massive air and naval power to silence Syrian artillery batteries, positioned in the Upper Metn mountains, just northeast of Beirut.