The Turkish foreign ministry said the detention of its citizens amounted to "banditry and piracy".
Gen Haftar's forces said on Friday they would attack Turkish targets over Turkish support for the internationally recognised Libyan government.
They also claimed they had destroyed a Turkish drone at a Tripoli airbase.
Libya has been torn by violence and division since long-time ruler Muammar Gaddafi was deposed and killed in 2011.
Gen Haftar started an offensive against the internationally recognised Government of National Accord (GNA), led by Prime Minister Fayez al-Sarraj, in April.
Why are Haftar and Turkey in conflict?
Turkey supports the GNA, supplying drones, weapons and trucks to boost its efforts in the ongoing conflict with Gen Haftar's forces, which control most of the east and south of Libya.
Gen Haftar's Libyan National Army (LNA) said it would strike Turkish vessels in Libyan waters and viewed Turkish businesses as targets.
It also banned commercial flights from Libya to Turkey.
Earlier on Sunday, Turkey said it would "retaliate in the most effective and strong way" to any threats from Gen Haftar's army.
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