BENGHAZI, Libya (Reuters) - At least 20 members of the Libyan National Army (LNA) have been killed and 40 injured in two days of fighting in the eastern city of Benghazi, a hospital official said on Wednesday.

The clashes come as the LNA, a force loyal to the country's eastern government, tries to extend its grip on the port city and dislodge the Islamist-dominated forces it has been battling for more than two years.

Led by Khalifa Haftar, the LNA has made major gains in Benghazi this year but still faces pockets of resistance. On Monday, it launched a fresh offensive in the Guwarsha and Ganfouda districts, carrying out air strikes and saying it had made some progress in ground fighting.

War planes could still be heard over Benghazi on Wednesday morning, and ambulances ferrying casualties raced through the streets. Roads were shut leading to western parts of the city where clashes were continuing.

At least seven militants were killed in Guwarsha on Wednesday, military spokesman Fadel al-Hassi said. Earlier casualty figures for the LNA's opponents were not available.

On Tuesday, a car bombing near a vegetable market at the eastern entrance to the city left 14 wounded, a second hospital official said.

Libya slid into political turmoil and conflict after long-time ruler Muammar Gaddafi was toppled in an uprising five years ago. In 2014, rival parliaments and governments were set up in Tripoli and eastern Libya, both backed by loose alliances of armed groups.

Haftar has become the dominant figure for factions based in eastern Libya. So far, they have opposed a government backed by the United Nations that arrived in Tripoli in March.

(Reporting by Ayman al-Warfalli; Writing by Aidan Lewis; Editing by Larry King)