Bilateral relations between Turkey and the U.S. were also discussed in the call, according to the statement.
The phone call came a day after a statement by an official loyal to the Libyan warlord Khalifa Haftar, which said the cease-fire is over and the war will continue in the embattled North African country.
Forces loyal to Haftar launched missile strikes to the south of Libya's capital, the military spokesman for the U.N.-recognized Government of National Accord (GNA) said late Tuesday, as the speaker of the pro-Haftar, Tobruk-based House of Representatives Aguila Saleh declared an end to a cease-fire in Libya late Wednesday.
Muhammed Kununu said in a statement that the Salah al-Din and Ramla regions south of the capital were hit by missiles, according to the media office of the Burkan Al-Ghadab (Volcano of Rage) operation.
On Jan. 12, the warring sides in the Libyan conflict announced a cease-fire in response to a call by President Erdogan and Russian President Vladimir Putin, and they gathered Monday in Moscow to sign an agreement aimed at ending hostilities and starting a political dialogue.
Following talks in Moscow, the head of the GNA, Fayez al-Sarraj, signed a cease-fire deal late Monday, but Haftar left for Libya early Tuesday without signing it after asking for more time to consider it.
The oil-rich North African country has been wracked by bloody turmoil since a 2011 NATO-backed uprising killed longtime dictator Moammar Gadhafi, with multiple foreign powers now involved.
The U.N.-recognized government had been under attack since last April from Haftar's forces, who is based in the east of the country.
Haftar's forces captured the strategic coastal city of Sirte on Jan. 6.
Sarraj Monday called on Libyans to "turn the page on the past, reject discord and to close ranks to move towards stability and peace."