European Union diplomats say sanctions against several Libyan ports, oil companies and more than a dozen other entities could be lifted as soon as Friday.
The EU's 27 members reached a preliminary agreement Wednesday in an effort to help Libya's National Transitional Council resume normal economic activity.
Diplomats say they expect a final agreement on Thursday to lift the sanctions the following day.
Search for Gadhafi
Meanwhile, thousands of Libyans have celebrated the end of the Muslim holy month of Ramadan in Tripoli's main square, as the country's provisional authorities press for the surrender of forces loyal to Moammar Gadhafi in his hometown of Sirte.
Anti-Gadhafi forces set up security around the Tripoli square Wednesday, including gunmen on rooftops, as several thousand people gathered to pray and express joy on the first day of Eid al-Fitr.
National Transitional Council leader Mustafa Abdel Jalil said his forces will begin military action in Sirte if pro-Gadhafi fighters do not complete negotiations and surrender by Saturday - after the three-day holiday.
The deadline relates primarily to Sirte, but also covers pro-Gadhafi strongholds in Bani Walid and the southern city of Sabha.
NATO says it has continued airstrikes on Sirte and Bani Walid, hitting multiple targets in both areas on Tuesday.
Neither the former leader nor his most influential sons have been seen since anti-Gadhafi fighters seized Tripoli last week. Some believe he may be hiding in the south.
Meanwhile, U.N. Secretary-General Ban Ki-moon says there is broad consensus that the international community needs to unite behind a well-coordinated plan for Libya's post-Gadhafi transition, and that the United Nations should lead that effort.
Ban told the Security Council Tuesday that the transitional government will outline its specific needs in the coming days, and that he hopes to get U.N. personnel on the ground as quickly as possible.
The secretary-general's special advisor on post-conflict planning, Ian Martin, said the U.N. effort will not involve peacekeepers, and that the NTC has made it clear Libyans want to "avoid any military deployment."
Gadhafi's daughter gives birth
Algerian officials said Gadhafi's daughter Aisha gave birth to a baby girl in an Algerian oasis deep in the Sahara on Tuesday. Algeria allowed some of Gadhafi's family members - including his wife Safiya, daughter Aisha, and two of his sons, Mohammad and Hannibal - to enter from Libya on Monday.
Algeria's U.N. ambassador, Mourad Benmehidi, said the group was allowed entry for "humanitarian considerations." Algerian officials have said Aisha's pregnancy was one reason for the controversial decision to take the family in.
In Washington, U.S. State Department spokeswoman Victoria Nuland said the Gadhafi family was under a U.N.-mandated travel ban. Nuland confirmed Tuesday that Algeria had sent a letter of explanation to the international community. She said Washington will decide how to respond after the U.N. and NTC review the letter.
The NTC has demanded that authorities in Algeria extradite members of the Gadhafi family.
Some information for this report was provided by AP, AFP and Reuters.