WASHINGTON, (Reuters) – The United States and Libya have agreed to try to resolve compensation claims from the 1988 Lockerbie bombing and other incidents Washington views as acts of terrorism by Libya, the State Department said on Friday.

The two governments this week opened negotiations seeking to lay to rest events that have bedeviled relations for decades despite the improvement in ties after Libya’s 2003 decision to abandon its pursuit of weapons of mass destruction.

“Representatives of the United States and Libya met in London May 28-29 to begin negotiations on a claims settlement agreement,” the two countries said in a joint statement issued by the State Department. “Both parties affirmed their desire to work together to resolve all outstanding claims in good faith and expeditiously through the establishment of a fair compensation mechanism.”

Two people familiar with the matter who asked not to be named said one idea that has been discussed would be the creation of a global compensation fund to pay families of the American victims of the incidents. These include 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. It has paid out $8 million per victim but has not made the final payment of $2 million.

A senior U.S. official said Libya had sought the global settlement talks out of concern about U.S. legislation that gave terrorism victims greater ability 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 U.S. official said that there were about eight other incidents involved in addition to those of Lockerbie, the Berlin disco and the French airliner but he did not provide details. 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 the North African country 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. “They (the Libyans) became concerned … and they came to us to suggest a new way to expedite resolution of all of the cases through a comprehensive settlement agreement,” said the U.S. official, who asked not to be named. He said Washington hoped to resolve the issues “in the shortest possible time” and with greater certainty than court cases and settlement talks, which have dragged on for years.

Jim Kreindler, whose law firm represents 130 of the Lockerbie victims and who chairs the plaintiffs’ committee of lawyers in the case, said he was pleased by the governments’ decision to open talks, but that his clients would insist on being paid the full $2 million they believe they are owed. “All of the clients will be glad to accept a mechanism where the U.S. government is involved in a global resolution provided that … results in the payment of the $2 million that is owed,” Kreindler said in an interview. “I don’t think any of the clients would accept a penny under $2 million.”