U.S. Assistant Secretary of State for Near Eastern Affairs David Welch is leading the U.S. delegation in the talks, said the official, who declined to be named because the discussions were still going on. The State Department had no comment.

At a meeting in London two months ago Libya presented what a U.S. official called a "comprehensive" deal to resolve a string of compensation cases which have soured relations between the former foes.

They include cases arising from the bombing of Pan Am Flight 103 over Lockerbie, Scotland, in 1988, which killed 270 people, including 189 Americans and the 1986 bombing of a West Berlin disco in which two U.S. servicemen were killed.

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 the German disco bombing.

The United States restored diplomatic ties with Libya two years ago after Tripoli gave up its weapons of mass destruction program in 2003.

Diplomatic sources said a fixed dollar amount was not included in the Libyan deal offered in March, which is aimed largely at speeding up the settlement of claims against Libya that have dragged on for two decades.

Tripoli's new offer follows U.S. legislation this year that expanded existing U.S. laws to enable terrorism victims to collect damages from governments like Libya by having their assets frozen.

In addition, a U.S. judge in January ordered Libya to pay billions of dollars in damages to relatives of Americans killed in a 1989 suitcase bombing of a French airliner over Niger.

The legislation and the January ruling angered Libya, which says it is being punished rather than rewarded for giving up its weapons of mass destruction program, a move that led to a thaw in relations.

In addition, U.S. companies seeking to trade with Libya say they are unable to do so because of fear of lawsuits that could be slapped on them by Americans seeking to freeze Libyan assets.

The Bush administration is trying to get lawmakers to exempt Libya from the new law and U.S. Secretary of State Condoleezza Rice has made clear she would like this issue to be settled.

Rice has held back from visiting Libya because of the compensation cases and other human rights concerns. She has said she still hopes to visit Tripoli before the end of the Bush administration's term in January 2009.