A column of black smoke billowed above the districts of cental Benghazi as the two sides battled with heavy weapons, witnesses said, and an old naval vessel in the Mediterranean port was set ablaze, apparently by shellfire.
The aim of the offensive, launched by forces loyal to retired general Khalifa Haftar backed by army units, was to "clear the zone of armed Islamist groups", said Colonel Ahmed al-Mesmari, armed forces general staff spokesman.
Earlier, the spokesman issued a call for residents to evacuate the Sabri district near the port, warning Islamist groups had "barricaded themselves among civilians" in the area.
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Last week, the pro-government forces recaptured areas in south and east Benghazi, including army camps seized by the Islamists in July when they expelled regular troops from most of the city.
At least 250 people have now been killed in government-backed operations launched in mid-October to defeat the Islamists, according to medical sources.
Islamist militias, including Ansar al-Sharia which is blacklisted by Washington as a terrorist group, have held sway in most of Benghazi for the past four months.
Libyan authorities have struggled to impose their will across a country awash with weapons and powerful militias which ousted longtime dictator Moamer Kadhafi in a 2011 revolt.
Militias now control large parts of the country.