ANKARA—Secretary of State John Kerry pressed Turkey's leaders to pull back from a string of inflammatory verbal attacks on Israel, as U.S. officials warned that Washington's ties with Ankara could suffer if the attacks continued.

The Obama administration's top diplomat met with Prime Minister Recep Tayyip Erdogan on Friday just two days after state media reported the Turkish leader, at a United Nations conference in Vienna, equated Zionism with fascism and referred to the Jewish ideology as one of the "crimes against...