Forces of Libyan commander Khalifa Haftar attacked opposition targets in Derna using aircraft and artillery, taking a wheat silo and villages on the outskirts, military officials said.
It was the first major operation since Haftar announced last week he would seize the last opposition stronghold to his Libyan National Army (LNA) in the east of the country.
The LNA surrounded the city, on the coastal highway between Benghazi and Egypt, and threatened to begin ground operations there. Its campaign was previously limited to occasional air strikes and bombardments.
Derna is controlled by a coalition of Islamists and rebel veterans known as the Derna Mujahideen Shura Council (DMSC).
After Libya split between rival camps in the east and west in 2014, Haftar gradually emerged as the dominant figure in the east. He is aligned with a parliament and government based in the east and opposes the internationally recognised government in Tripoli.
The United Nations is leading efforts to stabilise Libya and prepare for elections before the end of the year.
Egypt, which backs the LNA, carried out air strikes in Derna on what it said were training camps sending militants into Egypt.
Troops are advancing on five frontlines supported by air strikes and artillery, said Abdel-Karim Sabra, a spokesman for the operation.
The troops advanced to villages four km from the city, LNA sources said.
Sabra did not have casualty figures but websites close to the DMSC said five people were killed in air strikes.