A day earlier, a Turkish delegation paid a surprise visit to Tripoli where Cavusoglu discussed a lasting ceasefire and political solution in Libya.
Warlord Khalifa Haftar no longer has legitimacy in Libya and should not have a seat at the table, Turkey’s foreign minister said on Thursday.
"A coup plotter like Haftar, someone who claims to have seized the power, instead of a ceasefire, should not have a seat at the table. He should not be dealt with any longer,” Mevlut Cavusoglu said in a televised live interview on private broadcaster CNN Turk.
He also stressed that there is still no ceasefire in Libya even after the efforts carried out in Moscow and Berlin because of Haftar's attitude.
Warlord Haftar, whose militias are fighting the UN-backed Government of National Accord (GNA), left talks in Moscow without signing a Turkish and Russian sponsored ceasefire deal in January.
Cooperation with Libya
Meanwhile, Cavusoglu said security cooperation between Turkey and Libya's government may expand in the future.
"We had military agreements in the past. We had a memorandum of understanding. We updated one of them, resigned it. We signed it on the same day with the maritime jurisdiction agreement. The scope of the agreement may expand in the upcoming period," Cavusoglu said.
Last November, Turkey and Libya signed landmark pacts on military cooperation as well as boundaries in the Mediterranean.
Under the deal, Turkey has sent advisors to help the Libyan Army defeat warlord Khalifa Haftar's militias who is backed by Russia, Egypt, France and UAE.
The Libyan Army recently inflicted heavy blows on Haftar and liberated Tripoli and Tarhuna, in addition to other strategic locations, including Al Watiya airbase, from his militias.
The internationally recognised government has been under attack by Haftar militias since April 2019, with more than 1,000 killed in the violence.
READ MORE: Are Russian mercenaries abandoning Haftar?
Ankara-Washington joint work
During a webinar speech with the Turkish American National Steering Committee (TASC), Cavusoglu said that Ankara and Washington will cooperate in Libya in the upcoming period.
“We've received instructions to work together,” Cavusoglu said, noting that Turkey's President Recep Tayyip Erdogan and his US counterpart Donald Trump have a similar approach towards Libya.
President Erdogan indicated that "a new era" can begin in bilateral relations on the transition process in Libya after a phone call with Trump.
France responsible for chaos in region
Cavusoglu said that France is one of the countries supplying weapons to warlord Haftar and it is responsible for the chaos in Libya.
Cavusoglu also underlined that Paris will get a proper response if it tries to inspect Turkish ships.
Turkish military officials on Thursday firmly denied French allegations that Turkey had harassed one of its vessels taking part in a NATO mission in the Mediterranean.
“We are not a destructive and divisive country like France. If you treat a NATO ally like this, you get retribution. The necessary measures have been taken,” Cavusoglu said.
The allegations were baseless, and the Turkish Armed Forces have been a major contributor to the NATO military alliance for the past seven decades, said a senior Turkish official, who asked not to be named due to restrictions on speaking to the media.
"The Turkish Armed Forces has the experience to tell the difference between hazardous moves, harassment, friendly activities, cooperation, solidarity, and coordination," he added.