Undated (AP) _ Opposing factions of South Yemen's armed forces Wednesday fought for control of the Marxist country's capital, diplomats and sources in the region said. Some reports said forces loyal to the president, who reportedly made a televised appeal for calm, were making gains.

Arab diplomats in Sanaa, the capital of neighboring North Yemen, and shipping executives in the United Arab Emirates said artillery, tank and warplane battles were still raging Wednesday afternoon between government troops and even more radical Marxist rebels.

Other reports, however, indicated the fighting had lessened since Tuesday in the Soviet-allied nation at the southern tip of the Arabian Peninsula.

''The fighting has been sporadic throughout the day (Wednesday), somewhat less intense than yesterday (Tuesday),'' according to a Western diplomat in Sanaa, who was reached by telephone and spoke on condition of anonymity.

Reports on the fighting in South Yemen are often contradictory and have been impossible to confirm. South Yemen's communications links to the outside world, tenuous even in peaceful times, have been virtually severed for the past three days.

Meanwhile, the Bahrain-based Gulf News Agency quoted unidentified ''knowledgeable sources'' in Sanaa as saying South Yemen's President Ali Nasser Mohammed appealed for calm in a nationwide television address. Earlier reports had said he was seriously injured in the fighting.

The Kuwait News Agency, in a dispatch from Rome that quoted ''reliable sources,'' said Mohammed was ''in good health and was not injured'' and had spoken to the nation over an ''internal radio.''

''The rebels have become largely isolated and ineffective despite sporadic clashes in the harbor area,'' the Kuwaiti report said.

In London, Western diplomatic sources, who spoke on condition they not be identified, said there were indications the advantage may be turning toward Mohammed's supporters.

In New Delhi, South Yemen's Prime Minister Heider Abu Bakr al-Attas described the situation in his country as ''under control and getting better.'' Al-Attas, who was in India when the fighting began Monday, left for Moscow Wednesday but declined to say why he was going there.

Radio Moscow, citing unidentified news agency reports, said Wednesday night that Radio Aden had resumed broadcast after a temporary shutdown and government troops had restored control of South Yemen, after an attempted coup on Monday.

It said, however, that sporadic shooting still continued, and did not specify what it meant by government troops.

South Yemen is strategically located at the southern entrance to the Red Sea, which leads to the Suez Canal and the Mediterranean Sea. The Soviet Union has an important naval base in Aden, and the International Institute for Strategic Studies in London says Moscow stations 1,000 troops in the impoverished country.

Mohammed reportedly has been interested in improving ties with pro-Western Arab countries. The rebels apparently are hardline supporters of the Soviet Union, and some reports said Soviet troops were helping the insurgents.

Marine salvage executives based in the Persian Gulf said that wireless messages from ships that escaped from the port of Aden, South Yemen's capital, indicated the fighting was mainly between the navy and the air force against the army. Arab diplomatic sources gave similar reports.

In Djibouti, about 130 miles from Aden across a narrow strait, a Greek freighter captain said Wednesday that the ''air force and navy were together against the army. Who was the government side we do not know.''

George Bateras told The Associated Press in an interview aboard his 18,000- ton ship Telamon that the fighting around Aden harbor began Monday when three torpedo boats opened fire on some trucks that tried to enter the area.

He said tanks later joined the fight against the torpedo boats, which took cover behind anchored commercial vessels. A video tape of the battle provided by his crew showed torpedo boats firing on tanks on the pier. A tank exploded in one scene.

Persian Gulf-based diplomats who spoke on condition they not be identified said South Yemen's state radio remained off the air while telex and telephone links to Aden were still cut.

A clandestine rebel radio station broadcast anti-government statements and communiques about scattered fighting in Aden.

Western diplomatic sources in North Yemen said the rebel station may have been operating from a remote location in the country. They said it could barely be heard in the neighboring nation.

The sources said the station repeatedly broadcast a statement attributed to unidentified ''struggle leaders'' claiming that the four leaders of an alleged coup attempt were ''still alive.''

The state radio, shortly before it went off the air Monday, reported that the four had been executed and that Mohammed had survived an assassination attempt.

The state radio said the four included former President Abdul-Fattah Ismail, a hardline pro-Soviet politician, and Ali Antar, vice chairman of the Presidium.

The marine salvage executives said dissident pilots of the air force used Soviet-built warplanes to attack troops loyal to Mohammed at Khormaksar, site of Aden's international airport.

One Arab diplomat in Sanaa, who spoke on condition of anonymity, said the fighting had spread to all of South Yemen's six provinces.

According to diplomats in Bahrain, the Italian, British and Soviet embassies in South Yemen sustained unspecified damage as a result of this week's fighting and an Algerian diplomat was killed.

The United States has no diplomatic representation in South Yemen.

The newspapers Al-Ittihad in Abu Dhabi and Al-Siyassa in Kuwait said Antar was killed by two of Mohammed's aides during a meeting at party headquarters in Aden.

These and other Arab newspapers reported intermittent fighting around Aden, with rebels allegedly advancing on the presidential palace.