American policy faces a dilemma.
The Turks are a NATO ally whose reliability is an on-and-off thing unrelated to Turkey’s actual treaty obligations. The only reason Turkey is part of NATO is because somebody during the Cold War thought it would be a good idea to counter the USSR. With the USSR gone, Turkey is more like a dagger pointed at the heart of NATO, hence the delicate psycho-diplo-military dance NATO nations have had to follow for years, unwilling to cut Turkey loose from NATO, even now, as the Turkish government devolves toward authoritarianism and tighter ties with Russia. Putting it in perspective, Turkey’s longstanding, abysmal record on political and human rights is a prime reason that the European Union continues to deny Turkey EU membership. Turkey is not a truly modern state: Turks waged a genocidal campaign against its Armenian citizens a century ago, but it’s still against the law to mention that genocide in Turkey (by comparison, Americans can talk freely about the greater American genocide against native peoples, but the progress toward anything like justice is about the same in both countries).
The Kurds are for the Turks, metaphorically, the 21st century Armenians. The Turks exhibit all the signs of wanting to wage genocidal war on the Kurds but they are held off by multiple factors, not least the current taboo on genocide upheld by NATO and the EU, at least publicly, most of the time.