A Turkish police car parked at the entrance of U.S. consulate in Istanbul on Monday. (Ozan Kose/AFP/Getty Images)

When they met last month in New York, President Trump hailed what he called his “personal relationship” with Turkish President Recep Tayyip Erdogan and said the United States and Turkey were “as close as we have ever been.”

Erdogan called Trump “my dear friend Donald.”

Close observers of Ankara and Washington would have been ­forgiven for rolling their eyes. For the past several years, the ties between them have repeatedly frayed to near the breaking point, only to be temporarily patched. On Sunday, they snapped.

Following the arrest last week of Metin Topuz, a Turkish employee of the U.S. Consulate in Istanbul, the United States announced that it was immediately suspending the issuance of non-immigrant visas in Turkey. Ankara quickly responded with identical restrictions, suddenly upending the plans of countless Turkish and American tourists, students, busi­ness­peo­ple and others who did not already possess the necessary travel documents.

While the Turkish government provided no information about the Topuz arrest, the Daily Sabah, a pro-government paper, said in a Monday editorial that he was accused of “facilitating the escape” from Turkey of “known Gulenists” — followers of a U.S.-based Turkish cleric, Fethullah Gulen, whom Turkey accuses of being behind a July 2016 coup attempt.

On Oct. 8, U.S.-Turkey relations took a turn for the worse as both countries suspended most visa services. Here's a brief look at the events leading up to the diplomatic dispute. (Joyce Lee/The Washington Post)

That report and others provoked John Bass, the outgoing U.S. ambassador to Turkey, to post a 4½ -minute video on the embassy site to “explain” the visa suspension decision. Topuz, who worked in an office coordinating with Turkish law enforcement and ­“ensuring the security of American and Turkish citizens,” was the second such U.S. diplomatic employee arrested this year, Bass said, raising questions “about whether the goal of some officials is to disrupt the long-standing ­cooperation between Turkey and the United States.”

Without guarantees of Turkey’s respect for “the principles of rule of law that all modern democracies follow,” he said, the United States could not be sure its facilities were safe. He expressed hope the suspension of new visas at U.S. facilities in Turkey would not last long but offered no prediction.

Turkish prosecutors also said Monday in a vaguely worded statement that they had summoned yet another consulate staffer to testify. The statement mentioned that the staffer’s wife and son had been detained on Gulen-related allegations but did not say what charges, if any, the staffer faced.

Other than Bass’s video, neither the State Department nor the White House made any comment Monday on the Turkey situation. Erdogan, traveling in Ukraine, called it “saddening.”

But the administration’s sharp action appeared to mark a turning point in what Soner Cagaptay, a Turkish American political scientist at the Washington Institute for Near East Policy and author of a book on Erdogan, “The New Sultan,” called the long-standing idea “that the U.S. would cut some slack for Erdogan and look the other way” in the belief that its relationship with Turkey was bigger than the Turkish president.

The latest argument has exposed divides that began in the Obama administration and have become steadily deeper, despite Ankara’s initial optimism that Trump would be more to its liking.

President Barack Obama, Erdogan’s government had charged, was weak in executing their joint policy of supporting opposition forces fighting to oust Syrian President Bashar al-Assad and dragged his feet on Turkey’s request for Gulen’s extradition. Under Obama, Turkey believed, the United States was too supportive of Syrian Kurdish guerrillas fighting the Islamic State in that country.

“We have positive opinions of the new administration,” Prime Minister Binali Yildirim said in March, after Trump and Erdogan spoke by telephone during the U.S. president’s early weeks in office.

During the phone call, Trump was noncommittal when Erdogan warned the United States not to directly arm the Syrian Kurds, despite American military plans to use the fighters as its main ground force in a major offensive to clear the Islamic State from northern Syria, including the de facto militant capital of Raqqa. Turkey, Erdogan said, saw the Kurdish force as an extension of the Kurdistan Workers’ Party, or PKK, the separatist group in Turkey that both countries have designated as a terrorist organization.

By the time Erdogan visited Trump in Washington in May, the decision had already gone against him. There was talk that Turkey would retaliate by throwing U.S. forces out of its Incirlik Air Base, a central hub for U.S. attack aircraft operating against the Islamic State. Turkey, which had already sent forces into northern Syria to block Kurdish expansion close to its border, also threatened to block the U.S.-backed advance into Raqqa.

Neither of those things happened. But the relationship, already unraveling, was reaching a crisis point.

Turkish officials have also tried to win the release of Reza Zarrab, a Turkish Iranian gold trader facing U.S. charges of evading sanctions on Iran. Last month, U.S. federal prosecutors also indicted a former Turkish economy minister for allegedly conspiring with Zarrab.

Charges have also been brought in absentia against 15 Erdogan bodyguards who are accused of beating protesters outside the Turkish ambassador’s residence in Washington during the presidential visit in May.

Despite near-constant Turkish appeals, the administration has reported no progress in adjudicating its request to extradite Gulen, a permanent U.S. resident who lives in Pennsylvania. The Justice Department has not yet judged as sufficient evidence presented by Turkey describing a massive anti-government conspiracy. Since the attempted coup, tens of thousands of Gulen followers and ordinary critics of the government have been arrested.

That sweep has also ensnared a number of U.S. and European citizens, whose release Erdogan recently tied to progress on Gulen’s extradition.

In what was read in the United States as a gratuitous slap, Erdogan this month hosted Venezuelan President Nicolás Maduro on an official visit, just as the Trump administration called for other countries to reduce their ties with Maduro’s repressive government. Erdogan has also tightened links with both Iran and Russia.

As relations between the NATO allies worsen, their long-standing military ties — vital to the U.S.-led effort to eliminate the Islamic State from the region — have come under threat.

About 2,700 U.S. troops and civilians are based in Turkey, mostly at Incirlik, the air base near the Syrian border. The base also houses dozens of tactical nuclear weapons, said Kingston Reif of the Washington-based Arms Control Association. While instability is unlikely to threaten the weapons’ safety, he said, further political pressure from Ankara could restrict the Pentagon’s ability to deploy the F-15 and F-16 fighters capable of delivering them.

Retired Adm. James Stavridis, who commanded NATO under Obama and is now dean of the Fletcher School at Tufts University, described Incirlik as “beyond valuable” and urged that the United States “do everything we can to ensure we have a balanced, sensible and strategic relationship” with Turkey.

But Bulent Aliriza of the Center for Strategic and International Studies described the U.S.-Turkey relationship as one “born out of the mutual needs of the Cold War.” For years, he said, “the two sides have been making ad hoc efforts” to preserve a relationship whose reason for being has disappeared.

Now, he said, the “chickens are coming home to roost,” and “it’s difficult to see how to get back on an even keel.”

Fahim reported from Istanbul. Carol Morello and Alex Horton in Washington contributed to this report.