A military source said the clashes broke out yesterday when Islamist groups launched an assault on the headquarters of a special forces unit near the city centre, causing casualties among forces defending their barracks.
Benghazi's main hospital said the bodies of 28 soldiers had been taken there in the past 24 hours, along with 50 injured, while Al-Marj hospital, 100 kilometres (60 miles) to the east, spoke of two soldiers dead and 10 injured.
Overnight, special forces commander Wanis Abu Khamada told Libya Al-Ahrar television that his troops "still have the capacity to repel any attack on state institutions".
An AFP correspondent reported that several families could be seen leaving the area of the clashes, as loud explosions were heard in the city today morning.
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Near-daily clashes take place in Benghazi, where parts of the Mediterranean city have become strongholds for Islamist groups since the 2011 revolution that ousted longtime dictator Moamer Kadhafi.
London urged all those Britons currently in the country to leave, although its embassy in Tripoli remains open.
"Due to the ongoing and greater intensity of fighting in Tripoli and wider instability throughout Libya, the Foreign and Commonwealth Office (FCO) advise against all travel to Libya," the ministry's website said.
"British nationals in Libya should leave now by commercial means."
The United States evacuated its Libyan embassy staff under air cover yesterday as they faced a "real risk" from fierce fighting around Tripoli airport, Secretary of State John Kerry said.
The US announcement that it was evacuating its embassy came hours after the country's interim government warned that the clashes between militia vying for control of the strategic airport were threatening to tear Libya apart.