(Adds rival versions of how commander was killed)

By Ahmed Elumami and Ayman al-Warfalli

TRIPOLI/BENGHAZI, Libya, March 21 (Reuters) - Libya's official government conducted air strikes on Saturday against airports and a military camp in the capital Tripoli, controlled by a rival government, and killed a senior commander loyal to that government, officials said.

The internationally recognised government said on Friday that it had launched a military offensive to "liberate" Tripoli, which a group called Libya Dawn seized in August, reinstating a previous parliament.

The recognised prime minister, Abdullah al-Thinni, and the elected parliament have been confined to eastern Libya since then. Both administrations and the armed factions loyal to them are fighting for control, four years after Muammar Gaddafi was toppled.

A Tripoli official said Salah Burki, a Libya Dawn leader, had been killed west of Tripoli, where a state news agency reported clashes between Libya Dawn and forces from Zintan allied to Thinni.

Details were unclear. Another official and some news websites said Burki had been killed in an air strike on a military camp in Tripoli.

Saqer al-Joroushi, an air force commander loyal to the eastern government, said earlier that his aircraft had bombed Mitiga airport in Tripoli and a camp used by Libya Dawn near another airport in the capital.

He said they had also attacked the airport in Zuwara, a town near the Tunisian border, west of Tripoli. An airport official said the runway had been hit but there were no casualties.

On Friday, U.N. Special Envoy Bernardino Leon said the military offensive threatened international efforts to reach agreement in the next few days on a unity government and lasting ceasefire.

Talks are being held in Morocco, the latest in a series of meetings since September bringing together mostly moderates from both sides.

Western leaders say the U.N.-brokered talks are the only way to end the chaos in Libya, where Islamist militants have also gained ground. Both sides have attacked each other with warplanes in the past few days. (Additional reporting by Ulf Laessing and Omar Fahmy; Editing by Kevin Liffey and Stephen Powell)