"A delegation representing the government of (Prime Minister) Ali Zeidan came to meet us on Wednesday and asked us to lift the sieges but we refused," the militiaman told AFP outside the encircled foreign ministry.
"We will continue blocking (access to) the ministries of foreign affairs and justice until our demands are completely satisfied," he added.
Meanwhile, opponents of the sieges held protests in central Tripoli's Martyrs Square, waving signs calling for the respect of public institutions and denouncing the use of weapons to press any cause.
The gunmen have encircled the foreign ministry since Sunday and the justice ministry since Tuesday, to demand that the General National Congress adopt a bill that would purge former officials of the ousted regime of Muammar Gaddafi.
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The same groups, most of them former rebels who fought to oust Gaddafi in 2011, briefly occupied the finance ministry on Monday.
The GNC, Libya's highest political authority, has been studying proposals for a law that would see top figures from the Gaddafi regime removed from their posts.
Under increasing pressure from demonstrators, the GNC said on Monday that it was suspending plenary sessions until Sunday.
It said the delay was needed to give political blocs in the GNC time to examine the bill to reach a compromise on the law.
GNC Vice President Salah al-Makhzoum said a compromise had been reached among the political blocs by adding "exceptions" in the bill in order to retain key individuals.
He said the bill is expected to be voted on next week.
But the militiaman who spoke to AFP said the bill "falls below the expectations of the protesters" and has been "rejected" by a coalition of partisans of excluding former regime officials.