ISTANBUL — Turkey and the United States may embark on a new era in their relationship over the conflict in Libya, President Recep Tayyip Erdogan said after a telephone call with his US counterpart Donald Trump, adding that rebel commander Khalifa Hifter may soon be sidelined in diplomatic efforts to establish peace.

The two leaders also discussed protests against police violence in the wake of the killing of African American George Floyd in Minneapolis last month that have spread across the United States and to other countries, with Erdogan warning Trump that Kurdish militants were backing protesters in the United States.

In an interview with state broadcaster TRT late on Monday, Erdogan said Trump acknowledged Turkey’s success in reshaping the conflict in Libya, where the NATO member’s entry to support the internationally recognized government of Fayez al-Sarraj has dramatically shifted the war in his favor.

“A new period may begin between the US and Turkey regarding the [Libya] process, and we had some agreements during our conversation, and such a step could be taken,” Erdogan said without elaborating.