Speaking at a ceremony in Tripoli, Turkish Foreign Minister Mevlut Cavusoglu and Libyan Foreign Minister Najla Mangoush said they had signed memorandums of understanding aimed at benefiting both countries.
It was not immediately clear whether any concrete deals to emerge would include exploration in the "exclusive economic zone" which Turkey and a previous Tripoli government agreed in 2019, angering other eastern Mediterranean states.
That zone envisaged the two countries sharing a maritime border but was attacked by Greece and Cyprus and criticised by Egypt and Israel.
"It does not matter what they think," said Cavusoglu when asked if other countries might object to the new memorandum of understanding.
"Third countries do not have the right to interfere," he added.
Turkey has been a significant supporter of the Tripoli-based Government of National Unity (GNU) under Abdulhamid al-Dbeibah, whose legitimacy is disputed by the Libyan parliament, which backs an alternative administration.
Parliament Speaker Aguila Saleh, seen as an ally of Egypt, said the memorandum of understanding was illegal because it was signed by a government that had no mandate.
The political stalemate over control of government has thwarted efforts to hold national elections in Libya and threatens to plunge the country back into conflict.
(Reporting by Ahmed Elumami in Tripoli, Ayman al-Warfali in Benghazi and Ali Kucukgocmen in Istanbul; Writing by Angus McDowall; Editing by Ed Osmond)