An increasingly desperate Idi Amin appealed to five neighboring states today to pressure Tanzania to withdraw its troops from Uganda.

Reports circulated here that Amin has evacuated 80 relatives from his embattled country to escape the fighting, which poses an increasing threat-to his eight-year-old rule. Libya and Zaire were mentioned as possible sites of refuge, but here wants no confirmation of the reports.

Amin's army has been embroiled in heavy fighting with guerrilla forces, dissident army units and Tanzanian troops for several weeks, apparently a crucial phase of four months of hostilities involving his eastern African nation.

No official casualty tolls were available, but Tanzanian and Ugandan exile sources here claim Amin's army has lost about 3,000 troops since October and that most of his air force has been put out of action.

Most journalists are banned in Uganda and first-hand information was impossible to obtain. Both Dar es Salaam and Nairobi, the homes of thousands of exiles from Amin's brutal rule, were full of stories predicting his downfall. These reports obviously reflected the refuges' desire to see Amin driven from power. But the accumulation of information and Amin's own appeal for mediation by Kenya, Zaire, Sudan, Rwanda and Burundi clearly indicated the dictator's grip on power has grown fragile.

Residents of Kampala, the Ugandan capital, said tanks are stationed at key points throughout the city. Soldiers were said to be commandeering private cars and using them to transport their families to safety in neighboring Sudan.

[In Washington, the State Department urged all Americans in Uganda to leave if they can do so safely. About 100 U.S. citizens are estimated to be in the country.]

According to one reliable diplomatic source, Amin's army has constructed an elaborate defense position 25 miles outside Kampala on the road to Masaka. Guerrilla forces and rebellious army units announced yesterday that they control Masaka, but Amin claimed his troops recaptured the startegic southern town.

President Julius Nyerere of Tanzania challenged Amin today to allow observers into Masaka to prove the Ugandan Army is in control.

In a nationwide address, the Tanzanian president said the war with Uganda could end tomorrow if the Organization of African Unity would agree to condemn Uganda's aggression last fall into Tanzania. From the early stages of the conflict Nyerere repeatedly has stated that he will consider no appeal for restraint from any country that has not condemned Uganda for invading Tanzania. In fact, Africa has been generally silent, while the United States and many European countries have spoken out against Uganda's attack.

Nyerere also said Uganda must renounce any territorial claims on Tanzania and agree to pay compensation for damages caused during the October invasion into Tanzania.

An OAU ministerial committee has been meeting in Nairobi to discuss the conflict and shuttling between Dar es Salaam and Kampala. Amin has been calling for an OAU-supervised cease-fire and withdrawal of troops beyond their own borders.

Nyerere stated that he would be "very happy" to hear that Amin is out of power. He vehemently denied, however, that Tanzanian forces are attempting to oust the Ugandan dictator. He argued that Tanzanian troops are inside Uganda only to assure Amin does not try to seize part of Tanzania again. Nyerere contended that "only the people of Uganda" can overthrow Amin.

Although Nyerere draws a clear distinction between Tanzania's role and that of the Ugandan resistance groups backed by Tanzania, there can be no doubt that the casualties inflicted on Amin's forces by the Tanzanians have been the key factor in weakening the Amin regime.

Washington Post special correspondent Michael Dobbs reported from Belgrade :

According to an eyewitness account published in the respected Belgrade newspaper Polytika, machine-gun fire can be heard in Kampala almost every night. At the same time, howerer, everyday life seems to continue. In the smart downtown Hotel International, young couples dance and the streets are thronged.

Polytika's correspondent in Kampala, Petar Popovic, reported yesterday that it is difficult to establish just who is doing all the shooting and whom they are shooting at. "It comes from soldiers loyal to President Amin, including the armed patrols which have erected patrols on the approach roads to Kampala checking everybody who passes. But it also comes from army deserters, robbers, and members of the opposition Front for the Salvation of Uganda," he reported.

According to Popovic, the advance of Tanzanian troops allowed the Salvation Front to step up its disruptive activities in the capital itself. He reported seeing the naked body of a man killed just before dawn displayed at one of Kampala's busiest cross-roads. He was told that the man had been in uniform, but had not been able to prove his identity.