"We know that we have not solved all of Libya's problems today but we were aiming for fresh momentum," Merkel said.
Germany and the United Nations hope to persuade Russia, Turkey, the United Arab Emirates and Egypt to push their opposing camps to agree on a lasting truce in Tripoli, home to the internationally recognised government.
summit will put pressure on Khalifa Haftar and his eastern Libyan National Army (LNA) to halt a nine-month offensive against Fayez al-Serraj's government in the coastal capital after a week-long lull in fighting.
It is still unclear whether Haftar and Serraj will meet face to face.
Both of Libya's warring factions accused each other of violating a ceasefire proposed by Turkey and Russia, as fighting continued around the capital, Tripoli, on Sunday.
"Our politicians don't pay enough attention to foreign policy and they are paying the price for it." Arturo Varvelli
Turkey's decision to send the advisers and technical experts responded to a request by Prime Minister Fayez al-Serraj's GNA, which Ankara backs against forces allied to veteran commander Khalifa Haftar.
Sirte lies in the centre of Libya's Mediterranean coast, and has been controlled by GNA-aligned forces since they ejected Islamic State from the city with the help of U.S. air strikes in late 2016.
Tripoli, controlled by the internationally recognised Government of National Accord (GNA), is facing an offensive by military commander Khalifa Haftar's Libyan National Army (LNA) that began in April.
The cause of the rocket fire that shut the airport on Friday was not immediately clear.