WASHINGTON (AP) _ The Bush administration's campaign to improve ties with Ethiopia is getting a lift from reports that some 2,000 Cuban troops are preparing to leave the African nation.

The Soviet Union also is loosening its ties to Ethiopia, but hundreds of Soviet advisers and East German military and security personnel apparently will remain after the Cuban withdrawal.

The death in an airplane crash last week of Rep. Mickey Leland, a Texas Democrat who was a strong friend of Ethiopia in his crusade against hunger, sparked a cooperative search that also is helping to improve U.S. relations.

Senior State Department officials said they wanted to see the process accelerated. But, they said, two U.S. conditions must be met.

Those conditions are a continuing improvement in human rights and a serious effort by Addis Ababa to reconcile with separatists in Ethiopia's Eritrea region and an autonomous movement in Tigray.

But in a brief statement Friday, the State Department said it ''continues to support the territorial integrity of Ethiopia.'' That means the United States is opposed to a separate Eritrean state.

The prospect of Cuban troops leaving Ethiopia is also welcome news to the administration.

The Cubans are stationed in the Ogaden region, along the border with Somalia. In 1978 and 1979, Ethiopia used a force of 12,000 to 17,000 Cubans along with Soviet advisers to expel troops from Somalia.

The remaining Cubans mostly are on sentry duty. There is no sign that Somalia intends to become embroiled again in a conflict with Ethiopia.

Diplomatic sources, declining to be identified, said all the Cubans apparently would be withdrawn.

While Ethiopia does not receive foreign aid, it is eligible for humanitarian assistance. During a 1988 famine, the United States provided about $120 million - the largest outlay to any African country that year.

The fact that there are about 2,000 political prisoners in Ethiopia is considered a much larger obstacle to friendlier U.S. relations than the governing Marxist philosophy in Addis Ababa.