By Elise Labott, Barbara Starr & Nicole Gaouette / CNN  – 2016-07-19 05:29 GMT

Washington (CNN) — Turkey’s attempted military coup has brought its relationship with the US to a perilous crossroads. President Recep Tayyip Erdogan’s reaction to Friday’s unsuccessful coup is raising alarm bells in Washington as he undertakes a sprawling crackdown, demands extradition of a Turkish cleric from the US and suggests American involvement in the plot despite repeated US denials.

Washington has spent years trying to cultivate the Muslim ally sitting at the crossroads of Europe and the Middle East — a country crucial to the US fight against ISIS, stemming the tide of Syrian refugees and foreign fighters and tight military cooperation as a NATO member state. Now, there are fears that cooperation could slip and with it US interests.

The US, surprised by the coup and long concerned about Erdogan’s increasingly authoritarian tendencies, is trying to strike a tricky balance between opposing an undemocratic attempt to topple the government and pushing the government to ease up on its counter response.

The White House has watched Erdogan crack down on the independent pillars of a democratic state — including the judiciary, the media, political opponents and academics — with increasing concern.

“None of us have been under any illusions for some time” about Turkey’s increasingly undemocratic nature, said one senior State Department official, who described Erdogan as being “all about consolidating power.”

Turkish criticism of US raises tensions

At the same time, Turkish criticism of the US could well increase to the detriment of the countries’ ties.

“A radical expansion of power and authoritarian rule will come with the need to point to foreign and domestic enemies, and the US is foreign power par excellence in Turkey,” said Ambassador Jim Jeffrey, a former US envoy to Turkey. “They use us to gin up support.”

US and European officials are warning Erdogan not to go further down the road of authoritarianism or blame-shifting, issuing lightly veiled threats about the consequences, including potential disqualification from NATO.

Erdogan’s response to the crisis — either a tougher, broader crackdown or an attempt to reach out to Turkey’s divided constituencies — will redefine US-Turkey ties, analysts say, and could add yet another Mideast headache for the next US president to tackle in 2017.

“The relations with the US will be a subset of where Erdogan wants to take the country now,” said Jeffrey. “The coup is history. The question is what he does with it.”

The path he chooses could have particularly dire consequences for military cooperation.

Two defense officials told CNN there is a growing sense that much of the US military relationship with the Turkish military may have to be rebuilt following the attempted coup.

Given the large number of senior Turkish military officers arrested, one defense official said the question has become, “Who do we even talk to?”

And US officials privately point to Erdogan’s comments this weekend about cleansing the military to explain their concerns that he could use the attempted coup as an opportunity to consolidate power.

Already, there are worries that the Pentagon’s relationship with the Turkish military could suffer in ways that could affect US national security interests, including arms sales and future military exercises, as well as the fight against ISIS in neighboring Syria.

If Erdogan works at improving relations with other elements of Turkey’s political system, and doesn’t do permanent institutional damage, that will open the door to improving relations with the US and with the new White House occupant in 2017, Jeffrey said.

“If he continues his quasi-authoritarian government and Turkey becomes an institutionally limited democracy, that will mean a divided, weakened, dysfunctional Turkey, which we don’t need and will violate our values,” Jeffrey said. “We will have to react to that. It would be a recipe for worse relations.”

Kerry delivers warning to Erdogan

Secretary of State John Kerry issued a veiled warning to that effect at a Brussels press conference Monday, where his European Union counterpart Federica Mogherini warned that Turkish attempts to reinstate the death penalty in order to punish those accused of involvement with the coup could disqualify it from becoming an EU member.

Kerry delivered a reminder that NATO had standards for its members, too.

“NATO has a requirement with respect to democracy,” Kerry said. “NATO will measure very carefully what is happening and my hope is that Turkey is going to move in ways that do respect what they have said to me many times is the bedrock of their country.”

Kerry said that in three conversations with Turkey’s foreign minister in the last few days, “he assured me they fully intend to respect the democratic process and the law.”

But he warned that “the level of vigilance and scrutiny is obviously going to be significant in the days ahead” and cautioned against “a backsliding.”

A senior US administration official said Kerry was simply reiterating a long-standing message to ensure the Turkish government is aware of the need to preserve civil society and stand by the values in the NATO charter. At a time of fear, emotion and tension, it was important for Kerry to reiterate to Erdogan to “be careful not to overreach, which has been the basic thrust of our message all along,” the official said.

That official downplayed tensions between the US and Turkey, which have simmered over the past few years over differences on how to approach the fight against the Syrian regime and against ISIS, as well as Erdogan’s rule.

“It would not be fair for differences over domestic policies to cloud the fact that the strategic relationship has grown much closer over time,” said the official, who stressed “common interest and common effort” in the fight against ISIS, also know as Daesh.

Officials at the State Department were less circumspect.

“There is a worrying trend in Turkey about lack of freedoms,” this official said. “We have been expressing our concerns as much as we can, and with a NATO ally and a key partner in the anti-Daesh coalition, that gets dicey and uncomfortable.”

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So Kerry is delivering the message that “you can’t use this coup attempt to further crack down on freedom of speech, press and academic freedoms and civil society,” this official said.

If Erdogan ignores that warning at takes a more deeply authoritarian turn, relations with the US will get worse, Jeffries warned. In turn, Turkey will likely produce more open displays of direct hostility to the US.

US Ambassador to Turkey John Bass has already had to publicly rebut allegations from senior Erdogan government figures that the US was behind the coup or supported it.

“This is categorically untrue,” Bass said in a statement issued Monday. “Such speculation is harmful to the decades-long friendship between the two great nations.”

Turks have accused a Turkish cleric and Erdogan rival living in exile in Pennsylvania of being a key coup plotter. In a televised speech on July 16, Erdogan said that “if we are strategic partners,” the US would grant a Turkish extradition request for the cleric.

US wants evidence of cleric’s involvement

Both Bass and Kerry responded by making clear that the US has clear legal standards for such request that so far haven’t been met.

“We need to see genuine evidence that withstands the standard of scrutiny,” Kerry said. “Let me emphasize that we’ve never had such a request, we’ve never had such evidence.”

Jeffrey noted that the Turkish narrative about about Gulen “is the kind of thing that is done deliberately to gin up support.” And if Erdogan makes the argument that he is the only person to keep Turkey safe and on track, it would “exacerbate relations with the US. It will be difficult for us to put up with it and they will actively pick on the US as a reason for the crackdown,” Jeffrey said.

The most concrete impact may be on the military. The Pentagon will watch to see what officers are appointed to fill senior commander jobs in the Turkish military and determine how to interact with them.

An immediate test will come later this week when a Turkish military delegation is expected to show up in Washington for a counter-ISIS meeting with other nations in the coalition. Sensitivities are so high right now that the Pentagon will neither say who was scheduled to come or who might still be coming.

Jeffrey noted that the military is one of very few commonalities left in the US-Turkey relationship. “Our relationship with Turkey is almost entirely transactional with the military,” Jeffrey said.

There’s a little energy cooperation, very little trade and “there isn’t much left on values — the whole idea of a liberal democracy in the Middle East is gone.”

If political ties do get worse over the coming months, the next president will find it hard to continue good military relations, Jeffrey said, “because all decisions involving the US military realm are taken at the political level.”