On Thursday, Haftar's militia air force warned it would begin an "unprecedented" air campaign against Turkish forces in Libya, which have helped the GNA turn the tide in the war.
Sarraj's UN-recognized Government of National Accord has scored a series of successes in recent weeks in pushing back against warlord Khalifa Haftar, including seizing a strategic airfield near Tripoli on Monday.
Turkish Foreign Ministry spokesman Hami Aksoy on Thursday said Haftar's Libyan National Army (LNA) had received warplanes with "foreign support" and that they had vowed to target Turkish positions in Libya with an air campaign.
"Hereby, we once again remind that, if Haftar's putschist elements target Turkish interests in Libya, this will have serious repercussions and that we will consider them as legitimate targets". Presidential spokesman Ibrahim Kalin was quoted as saying by broadcaster NTV that attacks on Turkish positions would prompt heavy retaliation.
Haftar - who is backed by U.S. allies Egypt, the United Arab Emirates and Saudi Arabia - launched an offensive in April 2019 to seize Tripoli that has killed hundreds.
Since 2015, Libya has been divided between two governments; one based in the east and the other in the west, in Tripoli.
LNA spokesman Ahmed al-Mismari reiterated that there were 1,500 Turkish military personnel on Libyan soil, fighting on behalf of the GNA.
In what could be their most significant advance for almost a year, the GNA took control of the Watiya air base south-west of Tripoli on Monday.
The GNA also announced that it had regained control of two cities near the Tunisian border from Haftar's forces. Ankara's defence minister Hulusi Akar on Wednesday said that as a result of Turkish training and advice, "the balance in Libya changed significantly".
The LNA still holds all of eastern Libya and much of the south, including most oil facilities.
Haftar's forces have been receiving military equipment from Egypt and the UAE since 2014, and have been using aging Soviet-era jets from the military of Muammar Gaddafi, who was toppled in 2011.