Tanzanian-supported forces fighting to overthrow President Idi Amin continued their drive toward the Ugandan capital Kampala, but so far there has been no major battle or any sign of Amin's announced "counteroffensive."

According to Tanzanian and exile sources, the whereabouts of Idi Amin's army is something of a mystery.

Reliable sources say the antigovernment forces today reached Lukaya, halfway between Kampala and Masaka, the rear base for the Tanzanian and rebel armies. This puts the invading column considerably south of Mpigi, 23 miles from the captal, where Amin claimed a major battle forced the Tanzanians to retreat.

Western intelligence sources report there is no Amin stronghold anywhere along the route to Kampala. They say the antigovernment forces could drive straight into Kampala if they wanted to.

It is reliably understood that the anti-Amin column is covering only two to three miles per day, so as to avoid running head-long into Ugandan forces and to assure supply lines. Ugandan opposition sources say the area ahead of the column is being blanketed by artillery fire temporarily and that forward operators are warning villagers to evacuate the area.

Ugandan exile sources say the resistance army has had only minor skirmishes with Amin's soldiers. This raises the question of the whereabouts of both Amin's army, which numbered about 20,000 last October, and casts doubts on reports of Libyan reenforcements, estimated at about 1,500.

The fighting between Tanzania and Uganda began last October when Amin's forces invaded Tanzania and claimed a 710-square-mile section in the northwestern corner of the country. Initially, Tanzanian troops fought only to push the Ugandans back across the border. In early February, however, after repeated incursions by Amin's troops, Tanzanian President Julius Nyerere sent Tanzanian troops into Uganda to forestall, he said, another invasion.

The Tanzanians have been joined by hurriedly assembled armies of exiled Ugandans as well as soldiers and civilians from within Uganda. A halfdozen anti-Amin organizations are now involved in the fighting, the two largest of which are former Ugandan President Milton Obote's "national revolt" and the "Save Uganda Movement."

Obote states that he has received no word from the field of a counteroffensive, and he doubts one could have been launched yet, for several reasons. First, the Ugandan army is said to be not as well equipped as the Tanzanian, and there are reports that Amin's soldiers are reluctant to fight. Secondly, Amin claims to have captured Tanzanian artillery. The guerrilla forces are in front of the artillery, however, and Amin has not announced any heavy troop clashes.

Finally, there is no evidence that the Libyans are yet in place. Tanzanian and guerrilla sources say they have not yet come into contact with Libyan soldiers. Some exiles say Amin is keeping the Libyans in Kampala and the nearby town of Entebbe. There also are unconfirmed reports that the Libyans are refusing to go into battle.

One reliable source in Kampala told an exile organization here that the staff of the Libyan Embassy has left Uganda, but this could not be confirmed independently.

There is mounting evidence that Amin's own army is in disarray, and there have been reports that Amin's supporters and army officers are fleeing to neighboring Sudan.

But Obote cautions that it may be premature to announce the collapse of the Ugandan army. He points out that Amin's soldiers may be approaching the antigovernment column along secondary roads or through the bush given the slow forward movement of the resistance forces, however, it could take a week or more for any showdown to begin.