"I find myself compelled, despite opposition from my colleagues in recent days, to present (my resignation) voluntarily and without hesitation," Barghathi said, quoted by the official Lana news agency.
"I cannot accept the policy of force used by armed groups in our new state," he added.
Militiamen have surrounded the justice and foreign ministries since last week to demand the removal from public posts of former officials of the regime of slain dictator Moamer Kadhafi.
Initially, the gunmen intended to pressure the National General Congress, the highest authority in the country, to adopt the law on political exclusion.
But they remained camped outside the ministries despite the adoption of the legislation, with some of them now calling for the resignation of Prime Minister Ali Zeidan's government.
Today, a dozen vehicles armed with anti-aircraft guns and rocket-launchers were still parked in front of the foreign ministry, an AFP correspondent reported from the site.
"The employees and officials of the former regime who massacred the Libyan people continue to occupy important positions, especially the foreign ministry. The revolution has not come to this building."
Most of the gunmen had left the justice ministry, although five men in military fatigues posing as former rebels were still milling around the building's closed front door.
"We ended our protest. After the adoption of the law on political exclusion, we reached our goal. We just expect a ministry official to formally enter the building," said one of them.
"Two armed with anti-aircraft guns vehicles were still in the interior ministry, behind closed doors," he said.
Marghani added that "if this siege continues, we will study the possibility of moving the department to another district or another more secure city".
The controversial law passed by Libya's General National Congress is expected to take effect within a month.
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