By Ayman al-Warfalli and Feras Bosalum

BENGHAZI Libya (Reuters) - A Libyan navy ship was hit during heavy fighting with aircraft and tanks on Monday between the army and Islamist militants near the port of Benghazi, residents of the major city on Libya's eastern Mediterranean coast said.

The battle was part of a wider conflict in the North African state where former rebels who helped oust dictator Muammar Gaddafi in 2011 are fighting for power and a share of Libya's large oil revenues.

Army special forces, backed by troops of an ex-general, launched an offensive in the Benghazi area two weeks ago against Islamist militants blamed by Washington for a 2012 assault on the former U.S. consulate which killed the American ambassador.

A hospital next to Benghazi's port appealed to the Red Crescent to evacuate sick people trapped inside by the fighting while the army moved more tanks and artillery into the city.

A Reuters reporter could see smoke rising from the port, an important conduit for food, wheat and fuel supplies to eastern Libya. A security source said the unidentified navy ship was sinking but this could not immediately be confirmed.

Warplanes could be heard firing into the port area.

Dozens of residents were leaving Benghazi, heeding a call by the army to evacuate the port area and main commercial district where military officials said Islamists were holed up.

At least 238 people have been killed, eight of them on Monday, since the army started the offensive, medics said.

The army took a Reuters multi-media team to its Benghazi headquarters after wresting it back last week from Islamists. Many buildings in the vast complex were destroyed or burned out.

Libya is now split between rival tribes and political factions with two governments vying for legitimacy since an armed group from the western city of Misrata seized the capital Tripoli in August, forcing the internationally recognised Prime Minister Abdullah al-Thinni to relocate to the east.

The situation in Benghazi and other parts of Libya has been fluid with government forces unable to control militias.

Forces of ex-general Khalifa Haftar, which back the army in Benghazi, have planes from the Gaddafi-era air force though his foes say he also gets air support from Egypt, which is worried about the spread of Islamist militants.

Haftar denies having Egyptian military support.

(Reporting by Ayman al-Warfalli and Feras Bosalum; Writing by Ulf Laessing; Editing by Mark Heinrich)