Libya marks the second anniversary of the death of Muammar Gaddafi with the country on the brink of a new civil war and fighting raging in the eastern city of Benghazi, birthplace of its Arab spring revolution.

Violence between radical militias and regular forces broke out on Friday night and continued yesterday, while the capital Tripoli is braced for fallout from the kidnapping earlier this month of prime minister Ali Zaidan. Federalists in Cyrenaica, home to most of Libya's oil, open their own independent parliament in Benghazi this week, in a step that may herald the breakup of the country.

For months, radical militias and regular forces in Benghazi have fought a tit-for-tat war. Last week two soldiers had their throats slit as they slept in an army base. But Friday's killing of Libya's military police commander, Ahmed al-Barghathi, shot as he left a mosque, has became the trigger for wider violence. Hours after an assassination branded a "heinous act" by US ambassador Deborah Jones, armed units stormed the Benghazi home of a prominent militia commander, Wissam Ben Hamid, with guns and rockets.

Fighting continued into the night, with army units heading for the home of a second militia commander, Ahmed Abu Khattala, indicted by the US for the killing of US ambassador Chris Stevens last year. There, they were turned back by powerful militia units.

"There's fighting everywhere, checkpoints everywhere, I've moved my wife and children to somewhere safe," said one Benghazi businessman, Mohammed, who declined to give his second name.

Ben Hamid went on live television to insist he had no role in the killing of al-Barghathi, and vowed reprisals against those who destroyed his home.

Libya's militias are in the spotlight as never before, in a country racked by violence and economic stagnation. Zaidan has blamed the Revolutionaries Control Room, headquarters for the biggest militia – Libya Shield – for his kidnapping 10 days ago, promising harsh measures once the Eid religious holiday week ends.

Shield forces deployed in the capital denied staging the abduction, but their units were this weekend fortifying their positions in fear of attack.

The trigger for this spiralling violence was the arrest two weeks ago by Delta Force commandos of al-Qaida suspect, Anas al Liby, from his Tripoli home. That arrest has polarised opinion between supporters and opponents of Zeidan, and Nato, which bombed the rebels to victory in the 2011 Arab spring, has found itself in the hot seat over plans to train a new government army. Britain is to join the US and Italy in training Libyan army cadres at a base in Cambridgeshire.