Heavy fighting was reported yesterday in South Yemen, the only Marxist state in the Arab world, in what appeared to be an effort by a staunchly pro-Soviet faction to put the country more firmly under Moscow's influence.

Western embassies and shipping sources reported seeing bombing raids, artillery and tank battles, shelling by gunboats in the harbor, and street fighting between loyalist and rebel troops that continued into the night. Algeria announced that one of its diplomats was killed in the fighting.

Unconfirmed reports said President Ali Nasser Mohammed was shot and critically wounded Monday by Deputy Prime Minister Ali Ahmed Nasser Antar, allegedly one of four leaders of the rigidly pro-Moscow faction. South Yemen's state radio said Monday that Antar and the three others had been executed, but the radio made no broadcasts yesterday and western diplomatic sources said that there were indications that the four may still be alive and leading the coup attempt.

The prime minister of South Yemen, Haidar Abudakar Attas, was in New Delhi yesterday, after calling off a planned visit to Peking. Attas told reporters only that there was an "abnormal" situation in his country and that "when the situation becomes normal we will return."

South Yemen, one of the world's poorest countries, is strategically situated on the southern edge of the Arabian Peninsula, with a commanding position at the shipping channels connecting the Red Sea and the Indian Ocean, opposite the Horn of Africa.

Since 1979, when it signed a 20-year friendship treaty with the Soviet Union, South Yemen has served as an important Soviet naval and air facility. Soviet submarines use the harbor at Aden, the capital, between underwater patrols in the Indian Ocean and Soviet reconnaissance and cargo planes use air bases at Aden and on Socotra, a South Yemeni island 200 miles off the south coast.

U.S. officials reacted cautiously to the sketchy reports from South Yemen and were reluctant to speculate on their implications. South Yemen broke diplomatic relations with the United States in 1969, accusing Washington of being pro-Israeli and anti-Soviet.

State Department spokesman Charles E. Redman said that U.S. officials "have no independent confirmation" of the reports and he said there were "few, if any" Americans there. White House spokesman Larry Speakes said the United States was monitoring the situation "very closely" but that "we regard it as an internal matter."

Privately, U.S. officials made it clear that they preferred the incumbent government, which has shown willingness to work with the conservative Arab states, to the more radical faction attempting to overthrow it.

With normal communications lines cut and the country's international airport closed, the only reports filtering out yesterday came from embassies and from ships moored in the harbor.

Most reports indicated that South Yemen's 24,000-man military, armed by the Soviets and reportedly assisted by 1,000 Soviet advisers, had split, with part supporting Mohammed and part joining the opposition, headed by Antar and former president Abdul Fattah Ismail, who also reportedly was executed.

Sources quoted by The Associated Press said rebel troops and tanks were advancing on the presidential palace late last night, but there was no confirmation.

Four merchant ships, two of them Soviet, were on fire in the port, according to shipping sources. One shipping executive said that "fierce fighting has been raging in and around the port district." A Japanese shipping official said the Yemeni naval combatants apparently were using the cargo vessels as shields.

Diplomatic sources in Paris said the city convention center came under air attack by unidentified planes Monday, Agence France-Presse reported, and other sources said the airport was bombed yesterday.

British Foreign Secretary Geoffrey Howe, in Saudi Arabia yesterday after visiting Oman, another neighbor of South Yemen, said he was "in regular contact with our ambassador there" and that "the situation is very confused."

Other sources said the four British diplomats in South Yemen were restricted to the embassy, from where they could see ground fighting and air attacks.

South Yemen has had a bloody political history since gaining independence from Britain in 1967, with frequent assassinations and coups -- most of the trouble resulting from internal rivalries and chronic hostilities with neighboring North Yemen.

In one period of particularly concentrated turbulence in 1978, the presidents of North and South Yemen were assassinated within 48 hours of each other. North Yemeni President Ahmed Ghashmi, whose predecessor also had been assassinated, was killed when a South Yemeni official on a reconciliation mission opened a briefcase and it exploded. Two days later South Yemeni President Salim Robaya Ali was killed in a palace coup led by leftists loyal to Ismail who suspected Ali of being pro-Chinese.

When Mohammed, 49, came to power in 1980, after gaining control of the political apparatus, he exiled his predecessor, Ismail, to Moscow.

Since 1980, Mohammed, while maintaining his country's alliance with the Soviet Union, has relaxed many of the doctrinaire Marxist economic strictures, allowing limited private commerce and loosening import restrictions. He also has worked to improve relations with Saudi Arabia, Oman and North Yemen -- countries that Ismail considered too prowestern.