Tripoli, Libya (CNN) -- Despite the passage of a law banning Gadhafi-era officials from Libya's government, armed groups continued their blockade of two ministry buildings in Tripoli on Monday, this time demanding the dismissal of Prime Minister Ali Zeidan.
The adoption of the political isolation law by Libya's parliament on Sunday had been a main demand of militiamen who surrounded the foreign and justice ministries last week.
But on Monday some of the armed protesters said they want Zeidan out.
"We came out with two main demands, the political isolation law and the dismissal of Ali Zeidan's government," said Osama Kubbar, one of the leaders of the armed protest.
Kubbar said the protesters will not back down from this demand, and ministries will continue to be surrounded until Zeidan steps down.
According to Kubbar, indirect negotiations with officials close to the prime minister were under way. Last week two senior government confirmed talks with the leaders of the armed protests to try and resolve the situation.
On Sunday, a member of the General National Congress -- Libya's parliament -- told CNN that there were discussions among some lawmakers to withdraw confidence from Zeidan's government.
Kubbar accused Zeidan of being unfit to rule Libya, and some of the prime minister's official appointments were opposed by former revolutionary fighters. Zeidan's actions, Kubbar said, disrespected and provoked them.
He said his group protested peacefully for months, but when their demands were not met, they resorted to armed protests.
"(The government) forced us to do this. I hold them responsible; this is the only language they understand," he said.
Kubbar is the deputy head of an umbrella group created at the end of 2011 that includes several former rebel groups.
Many Libyans expressed concern on Sunday that the law's passage after months of political wrangling would undermine the democratic process and further embolden armed groups.
So far the Libyan government has said it will not use force in dealing with the armed protests to avoid bloodshed, according to recent comments from Zeidan.
"The government has so far shown a policy of restraint; they can actually confront if they chose to, but that would seem like a civil war broke out in Libya," said Mohamed Eljarh, a contributor to Foreign Policy magazine's "Transitions" blog. "I think that is why they're still showing restraint until now. Not sure how long for though."
According to Eljarh, the government has the support of some regional militias who could mobilize if there any efforts to remove Zeidan by force.
Like some other Libya analysts, Eljarh believes the armed protests are fueled by political interests.
He says leaders of the movement, such as Kubbar, ran in last year's parliamentary elections but failed to win a seat.
Kubbar also tried to become prime minister, but he could not secure enough parliamentary votes for a nomination.
"These guys aren't representatives of anyone but their own interests and agendas ... it is nothing to do with legitimacy, democracy or safeguarding of the revolution. ... To me, this is pure struggle for power and influence," Eljarh said.
Zeidan's government, in power since November, inherited a country awash in weapons and militias and has taken steps to try and rein in these groups as it struggles to build an army and a police force.
"Zeidan and his government took a tough line on militias in Tripoli and Benghazi, and they are now paying the price for such a line," Eljarh said.