State Department officials have had discussions in Washington this week with a top adviser to Libya's leader, Col. Muammar Qaddafi, about the current strained U.S-Libyan relationship, U.S. officials said yesterday.

Ahmed Shahati, former head of the Foriegn Liaison Bureau in Tripoli, met Peter D. Constable, the deputy assistant secretary of state for Near Eastern and South Asian affairs Thursday afternoon, officials said. Although Shahati no longer holds office, he is still believed to have much influence with Qaddafi. l

The United States ordered Libya's diplomatic mission here closed on May 6 and expelled the entire Libyan diplomatic staff, citing Tripoli's support of international terrorism and other "provocations and misconduct." Although the State Department has spelled out what actions by Libya's representatives here led to the expulsion order, officials privately cite investigations of official involvement in a campaign of intimidation against exiled Libyan dissidents, including the shooting of a Libyan student in Colorado last October.

U.S. officials also cite Libya's involvement in Chad, in the Lebanese missile crisis and its support of international groups. c

Libya has denied that it backs terrorist organizations, although it acknowledges support of what it considers legitimate nationalist groups such as the Palestine Liberation Organization and the Southwest Africa People's Organization in Namibia.

U.S. officials described Shahati's discussions here as "frank, but cordial," suggesting substantial disagreement on bilateral issues, and said the talks could not be considered negotiations. The Libyans requested the meeting, and State Department officials said they were glad to have a chance to discuss the current state of U.S.-Libyan relations.

Officials said the two sides discussed ways for the Libyans to represent their interests here. The United States is prepared to consider allowing the Libyans to open an interests section in another country's embassy here if Libya allows the United States to do the same, but officials said Tripoli does not yet appear ready to set up such an arrangement.

There are about 4,000 Libyan students in the United States and the Libyans are particularly interested in representing their interests. Some Libyan exiles are concerned, however, citing reports of involvement by progovernment students in Quaddafi's campaign against dissident exiles.

Last year, officials have said, 11 expatriate critics of Qaddafi were murdered abroad, mostly in Europe, and law enforcement officials believe many of the killings were politically motivated.

Despite the diplomatic strains between the two countries, Libya still supplies the United States with about 640,000 barrels of oil a day -- roughly a tenth of all U.S. oil imports -- and about 2,000 American oil technicians and their dependents live in Libya.