Israeli forces inched another block into Palestinian-held West Beirut tonight after a fierce battle with guerrillas near the Lebanese capital's racetrack.

The heavy exchange of shooting, which lasted about 90 minutes, began with small-arms fire and escalated into an artillery duel. The major fighting, which could be clearly seen and heard from the roof of the shell-battered Hotel Alexandre here in East Beirut, took place along the new tank and machine-gun positions that the Israelis established when they pushed one-half mile into the southeast portion of West Beirut at the museum crossing Wednesday morning.

The fighting shattered a relatively quiet day of minor incidents along the Green Line separating Israeli and Palestine Liberation Organization forces. To the west, Israeli warplanes bombed PLO positions.

The mass exodus that began yesterday of Lebanese civilians fleeing West Beirut continued throughout today. There was another massive traffic jam at Galerie Semaan, the only crossing into the east still kept open by the Israelis.

The fighting, which began in twilight at 6 p.m., started with brief bursts from automatic rifles and machine guns. They were quickly drowned out by explosions from mortar rounds and whistling rockets. About 20 minutes later, Israeli tanks and cannons joined the exchange. It could not be determined which side began the shootout, nor how many casualties were suffered.

Earlier in the day, it was clear that the Israelis have set up their lines several blocks west of the Green Line, east of the National Museum and a third of the way along the elliptical-shaped racetrack, known here as the hippodrome. One city block, the new no-man's land of snipers, separated the Israeli-PLO lines.

The latest heavy exchange of fire came amid mounting skepticism here among Israeli military officials and their Christian Phalangist allies that the besieged guerrillas would ever agree to withdraw peacefully from their West Beirut stronghold without a tangible political prize in return.

A PLO announcement that it was ready to withdraw from Beirut under four conditions was greeted here on the eastern side of the Green Line as a transparent ploy for more time.

A Lebanese forces official said he did not believe the PLO would withdraw because it has not won anything politically tangible, such as recognition by the United States. "Each side" in the negotiations, he said, "is caught in its own vicious circle" of unretractable positions.

"I believe the Israelis will take the PLO militarily, just as they have begun to do now--slice by slice," he said. "They will push the PLO deeper and deeper into West Beirut, like they were squeezing a lemon."

While residents of Beirut's east side went about their normal chores during most of the day, the war to the west was making a new impact on the sector, which previously had been largely protected from the conflict.

The fighting on Wednesday knocked out one of the city's major water mains and water service continued to be spotty in East Beirut today. Women and children carrying pastel-colored plastic containers collected water from neighbors and public spigots, a scene reminiscent of the western sector, where the Israelis periodically have cut off water supplies to pressure the guerrillas.

The predominately Christian eastern sector remained largely unscathed by artillery duels during the early weeks of the siege. But Israeli tank firing positions are located now in the heart of the sector's population centers, similar to PLO positions in West Beirut.

When the shelling started tonight, the streets and sidewalks cleared rapidly of civilians. Ten minutes after the fighting ended, however, traffic had returned nearly to normal.