Dawit Wolde Giorgis, head of the Ethiopian government's famine relief program, is reported to have been missing for more than three weeks since completing a fund-raising tour in Western Europe and the United States.

Western relief officials in Ethiopia, who are in contact with senior members of the government there, said Dawit is widely believed to be seeking political asylum in the United States.

A spokesman for the the U.S. Embassy in Addis Ababa said it had no information on Dawit's whereabouts and is not aware if he has asked for asylum. At the State Department, a spokeswoman said she had no report of Dawit being in the United States.

As commissioner of Ethiopia's Relief and Rehabilitation Commission, Dawit has become one of the most visible and widely quoted officials in Marxist Ethiopia during the past year. He has been an outspoken critic of western governments, charging they responded too slowly last year to Ethiopia's famine.

His defection would be likely to embarrass the Ethiopian government, which is a close ally of the Soviet Union and a frequent critic of the United States.

Dawit left Ethiopia Oct. 25 for a trip intended to raise aid donations for the famine, which is expected to continue through 1986. He reportedly visited Britain, Belgium, West Germany and the United States. He met officials in Washington and at the United Nations in New York. He was last heard from in Belgium and was expected to return to Ethiopia on Nov. 23, relief officials in Ethiopia said.

Dawit's brother defected from Ethiopia to the United States in September, according to diplomatic sources. The sources said he went to New York, where his wife had been given a job, through Dawit, with the Relief and Rehabilitation Commission.

Dawit's absence from Addis Ababa has delayed planning among the 35 countries and 47 nongovernmental organizations working there for next year's relief effort, aid officials say. The Ethiopian government has not made an official statement on Dawit.

A graduate of Columbia University Law School and a major in the Ethiopian Army, Dawit has been important to the government headed by his friend, Lt. Col. Mengistu Haile Mariam. During the early 1980s, Dawit served as governor of Eritrea, where rebels have been fighting the government since 1962.

Dawit headed the "Red Star" campaign against the rebels, which was unsuccessful and in which there were more than 30,000 government casualties. He subsequently was named to the number two position in the Ministry of Foreign Affairs.

Two years ago, Mengistu named Dawit as head of the government's agency responsible for coordinating famine relief. As commissioner of the Relief and Rehabilitation Commission, he was widely respected by western relief officials, who said he worked hard and was decisive.

In recent months, however, these relief officials said Dawit's influence in the government had waned. They said regional leaders of the ruling Workers' Party frequently overrode decisions made by the relief commission.

Dawit, who is divorced, is believed by relief officials to own a home in California.