Turkey has urged Libya to avoid any action that could lead to renewed conflict in the country.
The election was planned as part of a peace process to reunify the country after years of chaos and war following a 2011 Nato-backed uprising.
After a meeting of almost four hours chaired by President Tayyip Erdogan on Wednesday, Turkey's National Security Council (MGK) said a "calm in Libya that was achieved through big sacrifices" was an opportunity for peace.
The MGK called on parties involved in Libya to "refrain from steps that could cause new clashes" and urged authorities in the country to "follow democratic processes on a basis of legitimacy for the achievement of lasting peace and stability".
Turkey has provided military support and training to Libya's former internationally recognised Government of National Accord, helping it fight off an assault lasting several months on the capital Tripoli by eastern Libyan forces led by Khalifa Haftar.
Libya election cancellation - in pictures
It still has military personnel and Syrian militia fighters in Libya.
Ankara has supported the peace process but remained largely silent since the latest turmoil in Libya after the formation of two rival governments.
An interim Government of National Unity, which Ankara backs, was installed last year to oversee the run-up to elections and reunify divided state institutions.
When the elections collapsed, the House of Representatives parliament in the east, based in Tobruk, said the government's term had expired and it designated a new administration and set elections for next year.
However, the prime minister of the unity government said he would only relinquish power after elections, and armed forces backing each side have mobilised around Tripoli, raising fears of another conflict or a return to territorial division.
A date for a new election has not been set.