In a move that has eased rapidly growing tension with the United States. Ethipia's government chief has assured President Carter that his country does not intend to invade Somalia in its Soviet and Cuban-backed border war.

A White House announcement said "personal assurances" were given by Lt. Col. Mengistu Haile Mariam, the Ethiopian leader, to a U.S. mission headed by David Aaron, deputy assistant to the president for national security affairs. Aaron, just returned from Addis Ababa, briefed Carter on his mission yesterday morning.

White House sources said Mengistu did not promise the removal of foreign military personnel, officially estimated by the State Department at 1,000 Soviets and more than 5,000 Cubans, but emphasized that Ethiopia intends to maintain its independence and said that the reasons for the Soviet and Cuban help will no longer exist once its battle with Somalia in the Ogaden region is over.

The presidential emissary told Mengistu that the United States is not helping Somalia directly, indirectly or covertly, the sources said.

State Department spokesman Hodding Carter said the meeting was "helpful to both sides and augurs well for our relations in the future." Carter said the session "accomplished the mission of improving relations."

The most tangible indication of improvement was Mengistu's decision, announced by the White House, to receive a new U.S. ambassador "in the near future." The diplomatic post has been vacant since July, 1976, as relations between the longtime allies deteriorated.

The Ethipia-Somalia battle over the Ogaden region in southeastern Ethiopia took on expanding international significance as Moscow and Havana came to the aid of the Ethiopia's revolutionary government. Last Friday Carter warned that an Ethiopian invastion of Somalia could endanger "worldwide peace."

The United States has been gravely concerned about this latest Communist-backed drive in Africa, and it has caused alarm in Saudi Arabia, Iran, Egypt and some other U.S. allies in the area. At the same time, Washington has sought to avoid a commitment to the Somalia drive, which some American officials privately describe as "aggression," in order to prevent a dangerous superpower confrontation.

In recent days Washington publicly and privately drew a clear line at the international border, urging Somali forces to withdraw from Ethiopia and warning Ethiopia against pursuing its foe into Somali territory. Secretary of State Cyrus Vance met Soviet Ambassador Anatoly Dobrynin for a discussion expected to include this topic.

U.S. Soviet talks aimed at limiting military activities in the Indian Ocean have been recessed with no date for continued meetings set, according to an announcement yesterday. The U.S. has reportedly told the Russians that the talks are inappropriate while Soviet involvement in Ethiopia is growing.

According to a Pentagon announcement, a four-ship U.S. task force headed by a guided missile cruiser entered the Indian Ocean Monday. The Pentagon called it "a routine deployment."