President Reagan has given Marine commanders in Lebanon broad authority to use air strikes and artillery fire to help the Lebanese army and other units in the multinational peace-keeping force protect U.S. troops and embassy personnel, White House officials said yesterday.

The new instructions, under which the Marines no longer are limited to returning fire, were issued by Reagan after a series of weekend meetings in the White House and an appeal from Lebanese President Amin Gemayel to Secretary of State George P. Shultz last weekend for a wider U.S. role in Lebanon's battle against Syrian-supported militia forces, sources said.

White House spokesman Larry Speakes said the authority was issued at the recommendation of special envoy Robert C. McFarlane, a former Marine colonel, who is spearheading the U.S. diplomatic effort to end the fighting.

But other officials said the urgent Lebanese request for assistance played a key role. They said that "rigorous limits" had been placed on support for the Lebanese army, and that the support is aimed at protecting the strategic town of Suq al Gharb overlooking the Marine position at the Beirut airport.

The new orders came amid a flurry of other military and diplomatic efforts that included:

* A mission to Israel by Lawrence S. Eagleburger, undersecretary of state for political affairs, likely to begin today. Sources said Eagleburger wants Israel to encourage the Druze militia in Lebanon to stop fighting, but Israeli sources said Defense Minister Moshe Arens is reluctant to antagonize the large and loyal Druze population in Israel.

* An intensive diplomatic effort by McFarlane, who visited Saudi Arabia yesterday, to pursue a Saudi-originated plan for a cease-fire and new power-sharing negotiations between the Lebanese factions, with Syrian and Saudi participation.

* An administration attempt to muster congressional support for its diplomatic and military policies in Lebanon. House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) announced that the House will consider next week a resolution permitting Reagan to keep the Marines in Lebanon for another 18 months.

A strengthening of U.S. naval forces in the Mideast, possibly by the addition of the battleship USS New Jersey, now in the Atlantic. The battleship's 16-inch guns could hurl shells 25 miles onshore in support of the Marines while its 12 five-inch guns covered targets at closer range. The frigate USS Bowen, now off Lebanon, has one five-inch gun.

Administration officials differed on the likelihood of achieving a cease-fire in Lebanon.

In testimony before the Senate Foreign Relations Committee, Nicholas Veliotes, assistant secretary of state for Mideast affairs, said negotiations were at "a very delicate stage" that he couldn't discuss publicly.

The plan under discussion calls for a cease-fire followed by discussions between the Gemayel government and the opposing factions. The Syrian government wants to be involved in these discussions, and sources said the Gemayel government would agree, providing that Saudi Arabia enters the talks as a second outside force.

The main sticking point appears to be Syrian insistence that Lebanese armed forces adopt a "neutral" stance in any cease-fire agreement. This idea has been rejected by Gemayel as an unacceptable attempt to rob the Lebanese central government of power and authority.

Reagan's approval of U.S. aerial strikes and artillery support for the Lebanese army was viewed by administration officials as a display of U.S. backing for Gemayel. One official said it also was "a clear warning" to Syria that the Reagan administration does not intend to abandon its peace-keeping role in Lebanon.

In Beirut, the Central News Agency, which has access to Gemayel's inner circle, said the Reagan administration had promised aerial and artillery support for the Lebanese army.

"If any of the Lebanese army's current front lines in the mountains are penetrated, the Lebanese government can count on U.S. Navy air and artillery intervention," the news agency said.

Despite the new grant of authority, the Marines refrained from air strikes yesterday. Officials here said the new authority would "strengthen the resolve" of Lebanese forces and provide a warning to the Syrians.

U.S. commanders are not eager to use tactical air support in crowded Beirut because of the likelihood of civilian casualties, officials said.

Two British Buccaneer fighter-bombers based in Cyprus flew a rooftop sweep over Beirut yesterday in a show of force supporting the multinational force of U.S., French and Italian troops.

Offshore, western warships were shadowed by a Soviet missile frigate and a Soviet radio intercept ship, which were seen about two miles from the aircraft carrier USS Dwight D. Eisenhower.

At the White House, administration officials met late into the night to consider options in Lebanon amid reports that Pentagon officials had reservations about stepping up the U.S. combat role.

These officials said that McFarlane, backed by Shultz and subsequently by national security affairs adviser William P. Clark, had urged the broader authorization of U.S. firepower.

Secretary of Defense Caspar W. Weinberger and Gen. John W. Vessey Jr., chairman of the Joint Chiefs of Staff, were said to have expressed reservations about this escalation.

One source said Reagan had accepted McFarlane's recommendation with the understanding that it would improve prospects for a cease-fire.

Running through the internal debate was the warning by McFarlane and his supporters, sources said, that failing to do more to help Gemayel could jeopardize U.S. interests in countries as far away as the Persian Gulf. They said the United States would appear as an unreliable partner if it failed to give the Lebanese government extra assistance at this crucial juncture.

Sources also said Gemayel no longer is asking the United States or other countries contributing to the multinational force to send more troops to Lebanon.

Gemayel's new focus, sources said, is to get the multinational force, as presently constituted, to become more aggressive to combat anti-government forces, an escalation that U.S. leaders are resisting, according to administration officials.