Turkey's claims that the United States is supporting terrorists are "harmful to our relationship," the State Department said Friday.

"There's a lot of ludicrous statements ... out there about U.S. involvement in incidents and terrorist incidents in Turkey that are just, as I said, just beyond the pale," State Department spokesman Mark Toner told reporters. "They're not only not true, but they're harmful to our relationship."

Toner hastened to add that the comments "in no way" touch the foundation of the American relationship with Turkey, but his statement remains a rare public rebuke of a NATO ally. The comment came one day after Turkey's top diplomat wrote that "the Turkey-U.S. bilateral relationship is under severe strain," due to U.S support for a group of Syrian fighters tied to Turkish rebel groups.

Turkish President Recep Tayyip Erdogan made an even more dramatic claim. "They give support to terrorist groups including Daesh, YPG, PYD," Erdogan said last month. "It's very clear. We have confirmed evidence, with pictures, photos and videos."

Daesh is an alternative name for ISIS, the self-declared caliphate that took territory in Iraq and Syria and beheaded several American and western hostages in 2014. The YPG and the PYD are acronyms for Syrian Kurds, an ethnic minority along the Turkey-Syria border that the U.S. is working with in the fight against ISIS.

"The idea that the U.S. is not actively countering Daesh, for example, is ridiculous given all that we've accomplished over the past year-and-a-half in really reducing Daesh's foothold in Syria as well as in Iraq," Toner said.

The problem, in Erdogan's eyes, is that much of that fighting against ISIS has been conducted in cooperation with Syrian Kurds. Turkey regards the YPG as a white-label version of the PKK, a group of Turkish Kurds who have been at war with the central government for decades.

"While the US-YPG partnership has put considerable pressure on ISIS, the PYD's political ambitions inside Syria (matching closely with those of the PKK) pose a longer term threat to Turkish security," according to the Atlantic Council. "[The Syrian Kurds successes], however, have influenced the PKK's overarching ambitions in Turkey and, in turn, the Turkish government's assessment of the threat they pose."

The U.S. military angered Turkey once more by tweeting out a message disputing that the Syrian Kurds are affiliated with the Turkish Kurds. "The U.S. must stop trying to legitimize a terrorist group," Ibrahim Kalin, the press secretary for Turkey's president, tweeted in reply.

These disputes are exacerbated by the fallout from a failed attempt to depose Erdogan that was carried out by parts of the Turkish military. Erdogan blamed the coup on a Turkish leader who lives in the United States. He also instituted a crackdown on media and political dissidents in the aftermath of the coup, which the Obama administration has criticized.

"And, as the Turkish people who were victimized by the coup attempt understandably look for answers, we are lectured about due process, probable cause and evidential standards," Turkish Foreign Minister Mevlut Cavusoglu wrote in a Thursday column for the Washington Post.

The stakes of the disagreements have been raised, in recent months, by Russian President Vladimir Putin's efforts to woo Erdogan, even as Erdogan moves to change the Turkish constitution in a way that would allow him to remain in power until 2029.

"Turkey's increasing detachment from and disenchantment with the West mean Putin and Erdogan have more in common now than ever before," a pair of experts at The National Interest wrote in August. "If that reality is understood . . . and becomes the basis for joint policy, Western security and the stability of NATO will be weaker than at any time since the end of the Cold War."

At Friday's State Department press briefing, Toner ended his comments about Turkey on a conciliatory note. "We are cooperating with them, we are talking through these things, and this is what mature countries, democracies, do when they face these kinds of challenges; they talk through them," Toner said. "It's absurd to assume that countries, even allies, get along on every issue every day of the year. They don't."