ANKARA, Turkey — About the only thing the top diplomats from the United States and Turkey could agree upon on Friday was that their countries’ relations had reached a crisis point, as the two sides delayed negotiations until next month on issues that at times have brought the two NATO allies close to confrontation on the battlefield.

Secretary of State Rex W. Tillerson dined for three hours Thursday night with Turkey’s president, Recep Tayyip Erdogan, and diplomats from both countries labored into the early hours of Friday morning in hopes of announcing at least a few specific measures. But the joint statement issued on Friday contained only anodyne affirmations of respect and a promise to keep talking.

“All these mechanisms are not kicking the ball off into the corner, not delaying the process. We’re not trying to buy time,” said Turkey’s foreign minister, Mevlut Cavusoglu, while announcing an agreement that delays further talks until next month.

Gradually worsening for years, relations between the United States and Turkey reached a new low in recent weeks as Turkey began an offensive into western Syria to dislodge Kurdish forces there. While the Kurds have provided the bulk of the ground troops for the United States-led coalition battling the Islamic State militant group, Turkey considers them violent separatists and a threat to its national security.