WASHINGTON, Dec 21 (Reuters) - U.S. Secretary of State Condoleezza Rice said on Friday she wanted to visit Libya, saying it would be an "important step" in cementing ties with the former foe, but provided no date for a trip.

Libyan Foreign Minister Mohammed Abdel-Rahman Shalgam is set to meet Rice in Washington on Jan. 3, and Rice told reporters she was looking forward to going to Libya herself.

Libya has been pushing hard for a visit by Rice to Tripoli, which would be an obvious sign of closer ties between the two countries.

"I actually look forward to the opportunity to go to Libya. I think it will be an important step," Rice told reporters.

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 any final settlements resolving the 1988 Pan Am 103 bombing over Lockerbie, Scotland, as well as the 1986 bombing of a German disco. Americans were killed in both attacks.

Libya was implicated in both incidents and it had agreed to pay the families of Lockerbie victims $10 million per victim but has not made the final payment. It has also not paid compensation for U.S. victims of the La Belle disco bombing in West Berlin.

Rice said she was looking for an "opportunity to extend our relationship further," and pointed to Tripoli's closer ties to the West in general, including new investment opportunities in Libya, a major oil producer.

"Our promise had been to significantly improve U.S.-Libyan relations and to open -- help open the door, for Libya to receive investment and engagement with the international community," Rice said.

"It's why there are new investment opportunities in Libya, it's why so many companies are talking to the Libyans, it's why a number of leaders have been to Libya and the leader has been to other countries," she added, referring to Libyan leader Muammar Gaddafi.

If Rice visits Libya before President George W. Bush leaves office in January 2009, she would be the highest-level U.S. visitor to the country in more than half a century.

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