By Arshad Mohammed

WASHINGTON, Aug 27 (Reuters) - The United States wants Libya to resolve some long-standing issues, including two 1980s bombings, and has yet to schedule a visit by U.S. Secretary of State Condoleezza Rice, a senior U.S. official said on Monday.

U.S.-Libyan ties have warmed since Libya gave up weapons of mass destruction in 2003 but have been held back by the absence of final settlements of the 1986 bombing of a German disco and the 1988 bombing of Pan Am Flight 103 over Lockerbie, Scotland.

Libya, which was implicated in both incidents, agreed to pay the families of the Lockerbie victims $10 million per victim but has not made the final payment. It has not reached any deal to pay compensation for U.S. victims of the La Belle disco bombing.

Two U.S. servicemen were killed in the attack on the disco in West Berlin and 270 people, including scores of Americans, were killed in the Lockerbie bombing.

One sign of the limits on the relationship is the fact that no U.S. secretary of state has visited the North African oil exporter since John Foster Dulles went to Tripoli in 1953.

U.S. Assistant Secretary of State David Welch found a "positive spirit" among Libyan officials when he visited last week for talks that were to include a possible visit by Rice, said the U.S. official who spoke on condition he not be named.

"We haven't announced or scheduled anything yet, but we see increasing prospect that, at some point in the I hope not too distant future, there will be a Cabinet-level visit and I think it's appropriate that the secretary of state be the first one," he said.

"Between the desire and the fact there is still some work to be done."

The official declined to say whether progress on the Lockerbie and La Belle cases was a condition for a Rice visit but made clear the United States wanted to see some movement.

"I think the best environment for a successful visit would be one where there is progress on these bilateral issues," he said.

While Welch did not meet Libyan leader Col. Muammar Gaddafi, the official said Welch saw Libya's foreign minister, the heads of its intelligence services and two of Gaddafi's sons: Saif al-Islam, who is seen as Gaddafi's most influential child, and Mouatassam Gaddafi, Libya's national security adviser.

Last month Libya removed one major obstacle to better relations with Europe and the United States when it freed five Bulgarian nurses and a Palestinian doctor who had been convicted of deliberately infecting Libyan children with HIV.

The U.S. official said this seemed to have given confidence to Libyan officials who want closer ties with the West.

"It seems there is a positive spirit on their side," he said. "With the Bulgarian case now behind them, those who are advocating for change and opening up to the outside world more are feeling that they have some opportunities to move ahead."

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