Most are Africans intercepted off Libyan shores or inside the country as they prepared to board boats for Europe, Mohammed Abdelsalam al-Kuwiri said.
He said between 5,000 and 7,000 migrants have been held for months in 16 detention centres as Libya struggles to find planes to deport them.
The centres are mainly in the Tripoli region and in Misrata east of the capital, areas controlled by the powerful Fajr Libya militia alliance.
"Up to 7,000 migrants are held in these detention centres. They are given food, mattresses and medical care," he said.
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Last year, before Libya plunged further into chaos with two governments vying for power, authorities were able to deport illegal migrants on flights to their native countries.
But this is no longer the case, added Kuwiri, saying his government lacks the aircraft and does not have the means to deport them.
"European countries must help us with this burden and cooperate with us to return these migrants to their homes using European planes," Kuwiri said.
The United Nations says that more than 110,000 migrants transited Libya in 2014 en route to Europe.
Libya, with a coastline of 1,770 kilometres (more than 1,000 miles), has always been a stepping stone for Africans seeking a better life in Europe, with most heading for Italy.
People smugglers have exploited the chaos gripping Libya since the 2011 uprising toppled dictator Moamer Kadhafi to step up their lucrative smuggling business.