Zidan has been struggling with political opponents and militias since he was named a year ago by parliament to lead. The tensions were enflamed by last Saturday's raid by U.S. special forces that snatched a Libyan al-Qaida suspect known as Abu Anas al-Libi off the streets of the capital and whisked him off to custody in a U.S. warship.
The raid angered many militiamen, who accuse Zidan who has cultivated close security cooperation with the United States of collaborating in the abduction of a Libyan citizen. Zidan's government has denied any prior knowledge of the operation, but the raid appears to have prompted his abduction.
Several dozen of members of the hard-line Ansar al-Shariah group marched Friday evening between two main Tripoli squares, denouncing the raid and the prime minister. "Zidan, you coward, you are an American agent," they chanted, waving black banners. The al-Qaida inspired group is believed to be involved in Sept. 11, 2012 attack on a U.S. diplomatic post in Benghazi that killed the ambassador and three other Americans.
Along with other militias, Ansar al-Shariah held a larger protest, backed by pickup trucks mounted with machine guns, in Benghazi.
In Tripoli, al-Libi's family attended a separate rally by about 50 Islamists. His wife told The Associated Press, "The Americans "are the terrorists."
"For six days I have no idea if he (al-Libi) is alive or dead, sick or well," she said, identifying herself as Um Abdullah and speaking from behind a black veil over her face. "I want to talk to him because even if they say he is fine, I don't believe the Americans."
Al-Libi whose real name is Nazih Abdul-Hamed al-Ruqai, is accused by the U.S. in connection with the 1998 bombings of its embassies in Tanzania and Kenya.
At the same time, Prime Minister Zidan faces criticism from many Libyans who hate militias and say he has proven impotent to stop them.
"Zidan shows up as a helpless guy who doesn't have confidence," said young businessman Hazem al-Tamami, watching the prime minister's speech at a cafe. Referring to the militias, he added, "If you ask me, I will bring an Apache and bomb them all."
Militias originated in the "revolutionary" brigades that fought Gadhafi's forces. Since his ouster, they have refused to disarm and have mushroomed in size and power. Many have been enlisted by the state to serve as security forces, since the army and police are weak, underequipped and under-paid. But they often continue to act as armed vigilante factions with their own interests, and some follow radical al-Qaida-style ideologies or are believed to have links to the terror organization.
Touting themselves as "revolutionaries," some have long demanded Zidan's removal for accepting Gadhafi-era officials in government posts. Zidan himself served as diplomat under Gadhafi before defecting to the opposition decades ago. Militias have in the past besieged government buildings and carried out kidnappings including one last month of the defense minister's son, apparently to pressure him against trying to rein in the groups. On Friday, the military held memorial for killings of 16 Libyan soldiers in a checkpoint near Tripoli by suspected militants days ago.
In his speech, Zidan warned that "there are those who want to take Libya into the unknown. They want to turn Libya into Afghanistan or Somalia."
He said armed groups use violence to press individual demands and block the establishment of the police and military. "We want a nation of institutions, with an army and police," he said. "But there are those who want to terrorize the state and the courts and the institutions, and this we refuse."
He vowed that those involved in his abduction would be punished. He said the attackers looted everything in his room, from cellphones and documents to even his underwear.
Zidan said his captors told him they belonged to the Libyan Revolutionaries Operation Room, an umbrella group for various militias, including Islamic hard-liners. The agency was created by Nouri Abu Sahmein, the head of the parliament or National Congress as a parallel security force for the capital. That has raised questions on whether they acted on orders from Abu Sahmein, who belongs to an Islamist faction.
Zidan said his captors told him they were acting on orders of their leaders. But he did not specify Abu Sahmein, who visited him while being held, and thanked him for his help in ensuring his freedom.
Earlier, the Operation Room in its official website accused Zidan's government of "collaboration" in the U.S. raid.
Another militia group called the Anti-Crime Department was also involved in the abduction. Its spokesman, Abdel-Hakim al-Balazi, said that the Operation Room members brought Zidan to one of their buildings, claiming they had a warrant for his arrest.
Al-Balazi questioned why parliament chief Abu Sahmein didn't immediately free Zidan when he visited him in the cell.
"I am personally surprised. How come you are the president and you see your prime minister held in a prison and you just leave," he said.
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Keath reported from Cairo.