Street battles between Moslem militiamen fighting for control of west Beirut continued today, further delaying a trip to New York by British church mediator Terry Waite for planned meetings with State Department and White House officials.

Waite, a lay representative of Archbishop of Canterbury Robert Runcie, the spiritual head of the worldwide Anglican communion, was stranded at the Commodore Hotel for the second straight day by the latest spasm of violence in the Lebanese capital.

During a brief news conference this morning, held against the background of thunderous clashes involving truck-mounted rocket launchers, antitank grenades and machine guns, the church envoy said that he had "two further face-to-face" meetings this week with the captors of four American hostages. This was his second visit to Beirut in the past 10 days as part of accelerated mediation efforts to seek the hostages' release.

The composed and relaxed emissary spent most of the day resting in his hotel room and listening to music by Robert Schumann on a portable cassette player as Druze and Sunni Moslem militiamen swarmed into the lobby of the Commodore, taking combat positions at the doorstep.

Hooded gunmen had climbed up a wall surrounding the hotel and jumped into its small garden to launch a noisy offensive with shoulder-mounted Energa recoilless rifles, rocket-propelled grenades and machine guns against Shiite Moslem militiamen holed up in a building across the street.

Waite left his room only for a 15-minute briefing to the press and a lunch of lentil soup and a small hamburger with a group of reporters trapped by the fighting. Disclosing no details about his secret mission, he described the hostilities as a "tragic sideshow" that he could do nothing about.

As night fell, a Syrian-mediated cease-fire took hold and militia commanders roamed the ravaged streets of west Beirut to call on their fighters to go home. Gun battles apparently triggered by inter-Moslem bickering over display of the Lebanese flag deteriorated into an all-out war between the Shiite Amal militia and its allies on one side and Palestinian-trained Druze fighters supported by Sunni gunmen on the other.

Druze objections to the red, white and green Lebanese flag and a drive to tear it down from schools and government buildings to replace it with the red banners of the Druze Progressive Socialist Party for Lebanon's independence day set off the fighting yesterday and today.

Sunni militiamen from the underground Mourabitoun -- Arabic for ambushers -- joined with the Druze to flush out Shiite Amal fighters from west Beirut neighborhoods previously dominated by the now-outnumbered Sunni community.

In some districts, the Druze party and its allies used tanks. Local radio stations reported that the Druze opened up with artillery and field guns from the hills overlooking the city. Druze sources said the party had to bring in 50 militiamen by sea from the coastal town of Damur to reinforce its units. Fires caused by rockets and antitank missiles spread in residential areas and gasoline stations, as street fighting prevented rescue workers and firemen from moving toward the fires.

The arrival in Beirut of a representative of Syria's intelligence chief in Lebanon, Ghazi Kanaan, and his meeting with Shiite Cabinet minister and Amal leader Nabih Berri paved the way for a cease-fire. The Sunni prime minister, Rashid Karami, and Lebanon's grand mufti, Sheik Hassan Khalid, issued an appeal for an end to the fighting earlier today.

Initial casualty tolls said there were at least 150 dead and wounded.

The effects of this latest round of fighting on a stumbling Syrian-sponsored package of political and security reforms for Lebanon remain unknown. The new Sunni-Druze alliance demonstrated, however, mounting fears of growing Shiite influence. The Shiites are the largest single community in Lebanon, constituting about one-third of the total population of 3.5 million.

Sunni combatants entered the fight to avenge a crushing defeat dealt to them by Amal last April -- ironically, with the help of the Druze. A Sunni commander at the entrance of the Commodore Hotel said the flag controversy was not the real cause of the fighting. He said the Sunnis were fighting to drive Amal out of parts of the city in hopes of "doing away with sectarianism and putting an end to the harassment" of ordinary citizens at the hands of the Shiite militia.

The fiercest gunfights took place in the Ras Beirut district and spread to the strategic Murr Tower overlooking the old Jewish Quarter and the battle-scarred hotel area just west of the Green Line dividing Christian east Beirut from the largely Moslem western section. Militiamen battled for control of the unfinished 40-story building, until now an Amal stronghold, where stolen cars and kidnaping victims are kept.

Minutes before announcement of the cease-fire, a Druze militiaman crouching behind a wall outside the hotel said his men had succeeded in routing out Shiite gunmen from the once-fashionable Hamra shopping area. "Amal are running now, they are running away," he said with a nervous, mirthless laugh.

It was not clear which traditional strongholds had been overrun throughout the city. A Druze spokesman, Jihad Zuhairi, confirmed to reporters in the afternoon that Amal fighters had succeeded in taking control of the Druze-held Beaurivage area in Beirut's southern outskirts.

Residents pinned down in an apartment near the American University of Beirut said about 100 Druze militiamen wearing red armbands had advanced from the seafront and surrounded Amal fighters in their area.

For once, camera crews and photographers did not have to go out on the streets and brave shellfire to get their footage and still pictures. This latest episode of militia warfare came to their doorstep, enabling them to work within the relative safety of their hotel walls.

The militiamen also made themselves at home, strolling in casually for soft drinks and refreshments at the hotel bar or from the kitchen.

One commander stopped the battle for a few minutes for noontime prayers on the turquoise-and-red carpet of the glassed-in Commodore lobby.

Carrying their ammunition supplies in plastic bags, the militiamen, encouraged and excited by the clicking of French photographers and the spotlight held up for television cameras, put on their best show.

Waite, unruffled and unperturbed by crashing glass, chipped masonry and flashes of green and orange trajectories from weapons fired from around the hotel, said in an interview that he was very "pleased" with his contacts thus far.

"I am able to say that progress is being made," he said, although "it might appear for some that a point of deadlock has been reached in this matter. While I do not deny the great difficulties facing me with this problem, I do believe it can be resolved."

He noted that a great deal of work would still be involved, requiring the good will and support of others.

Islamic Jihad, the underground organization holding the kidnaped Americans, is demanding the release of 17 comrades held in Kuwaiti jails on bombing charges since December 1983. The Anglican Church envoy, when asked whether new conditions had been introduced by the captors, replied: "No, we are still in the same position." He did not rule out travel to another country after the United States, but he refused to be more specific.

Waite said he would in no way put himself in a position to exert pressure on the Kuwaitis. He said, however: "I think I can find a formula that perhaps will help us through."

Waite said he would leave Beirut Sunday for New York for meetings with White House and State Department officials with whom he has met before on the American hostage crisis. He told reporters that he had appealed to the Americans' captors not to harm them and had been assured that they were all right.

"I would say that the situation remains dangerous, and false steps, however well-intentioned, with the process I have started really could end in disaster," Waite cautioned. "The way ahead is difficult but by no means impossible."