It was a rare visit by a senior US official to Libya, which is currently split between two competing administrations.
The Tripoli-based government said CIA director and Prime Minister Abdul Hamid Dbeibah discussed co-operation, economic and security issues.
It posted a photo of the two shaking hands on its Facebook page.
The Libyan government gave no indication as to when the meeting took place. There was no immediate comment from Washington about the trip.
Mr Burns’s visit followed last month's surprise extradition of a former Libyan intelligence officer accused of making the bomb that exploded on a commercial flight above Lockerbie, Scotland, in 1988, killing all on board and 11 people on the ground.
Washington last month announced Abu Agila Mohammad Masud, wanted since 2020 by the US over his alleged role in bringing down the New York-bound Pan Am flight 103, was in their custody and would face trial.
His handover by Mr Dbeibah’s government raised questions of its legality inside Libya, which does not have a standing agreement on extradition with the US.
Mr Dbeibah’s mandate remains contested after planned elections late last year did not take place.
Torn by civil war since a Nato-backed uprising against former autocratic ruler Muammar Qaddafi in 2011, Libya has for years been divided between rival governments in its east and west, each backed by international patrons and numerous armed militias on the ground.
Militia groups have amassed great wealth and power from kidnappings and their involvement in Libya’s lucrative human trafficking trade.
Amid the chaos, in 2012, a terrorist attack on the US consulate in the Libyan city of Benghazi killed four Americans, including US ambassador Chris Stevens.