At Incirlik, the United States has based A-10 attack planes, KC-135 refueling tankers and surveillance aircraft, including armed drones. The Air Force has said American refueling aircraft at Incirlik handle roughly one-third of refueling operations for the air war over Iraq and Syria.  Use of the base increased the length of time that American and other allied warplanes could remain over Iraq and Syria. The manned and unmanned strike missions, as well as surveillance missions, from Incirlik — all hours closer to the fight than aircraft in the Persian Gulf — have made a big difference. Losing that advantage would significantly hamper operations, American commanders say.  At Diyarbakir, another Turkish base, the Air Force began staging small numbers of American troops last fall to recover any downed pilots or flight crews. The Pentagon’s plans to place a mobile rocket system known as Himars, short for High Mobility Artillery Rocket System, somewhere in Turkey to support United States operations in Syria could also be in jeopardy.  The Turkish military, which sees itself as the guardian of the secular state, has overthrown or forced out four elected governments since 1960. Turks have long been fascinated by what they call “the deep state”: a murky group of operatives, linked to the military, thought to have battled perceived enemies of the state since the Cold War.  But in a striving Turkey of thriving capitalism and a still boisterous news media, memories of the damage to democracy fomented by past coups remains strong. In the first coup of 1960, the military tried the prime minister and president for treason. The 1980 “September 12 Coup” helped end a period of anarchy and terror, but not before thousands of people were arrested and dozens were executed and tortured.  Analysts said the latest coup attempt underlined the extent to which elements within the military had become frustrated by Turkey’s direction under President Recep Tayyip Erdogan, a religious and conservative Muslim. Mr. Erdogan came to power in 2002, pledging to declaw the once powerful military. He proceeded to impose civilian rule over the state by putting dozens of prominent generals and officers in prison after dramatic show trials for treason, often on tenuous and even fabricated evidence.  Moreover, Mr. Erdogan, whose government once promised a foreign policy of “zero problems with neighbors” has seen conflicts multiply, including 14 attacks on Turkey in the past year by Kurdish and Islamic State militants. He has presided over an increasingly shaky economy, and alienated allies from the United States to Russia. His government has been mired by accusations of corruption.  American and NATO officials have been pressing to insulate the mission against the Islamic State at Incirlik and other Turkish bases from the internal upheaval. But even if they succeed, Turkish politicians and security forces are likely to be, at the very least, distracted from their counterterrorism focus despite recent vows to redouble efforts after last month’s Istanbul airport bombing.  “They’re going to be focused on rooting out coup plotters, and that’s going to preoccupy all the national security services; and everything else, including going after ISIL, will be secondary,” said Eric S. Edelman, a former United States ambassador to Turkey and top Pentagon official under President George W. Bush. “It may affect their ability to protect themselves from ISIL blowback in Turkey.”  One big concern expressed by officials and analysts is that Mr. Erdogan will freeze the cooperation against the Islamic State while he sorts out who in the military supported and carried out the coup attempt. If the Turkish military fractures further — whether through arrests, forced retirements or other actions — it could become a weakened partner in the fight against the Islamic State.  A failed coup attempt on Friday night has gripped Turkey. By Saturday morning, thousands of soldiers had been detained, accused of trying to overthrow the government, and civilians were left in a state of unease.  “This could really effectively eat into the institutional durability of NATO’s second-largest military,” said Soner Cagaptay, a specialist on Turkey at the Washington Institute for Near East Policy.  Aykan Erdemir, a former member of Turkey’s Parliament who is now a senior fellow at the Foundation for Defense of Democracies in Washington, said the coup reflected the extent to which the Turkish military, a hierarchical top-down organization that controls one of the biggest armies in the region, had become deeply polarized under Mr. Erdogan.  He said simmering frustration among some within the officer class, chief among them the coup’s suspected mastermind, Col. Muharrem Kose, had finally boiled over.  Jane Kandur, a member of Mr. Erdogan’s Justice and Development Party’s Istanbul branch, said by phone from Istanbul that the “failed coup” was “an attempt by Gulenists in the military to hold on to power they don’t have the right to have.” She was referring to followers of Fethullah Gulen, a Muslim cleric living in exile in Pennsylvania.  But others cautioned that the bloodiness of the coup, including the targeting of civilians, was outside the traditional methods of the Gulen movement, which has typically used the news media, the judiciary and the police to damage opponents.  Dani Rodrik, a prominent economist at Harvard’s John F. Kennedy School of Government, predicted that Mr. Erdogan would use the coup as a pretext to move forward with his ultimate aim of a full presidential system of government in Turkey.  “This will do wonders for Erdogan’s cult of personality,” said Mr. Rodrik, whose father-in-law, a retired general in Turkey, was accused of leading a plot to overthrow the government before being freed from prison and acquitted. “It makes Erdogan’s quest for an authoritarian presidency virtually unstoppable. I fear I will not see a democratic Turkey in my lifetime.”  Whatever happens, veteran Turkey watchers said they were flabbergasted by the coup attempt, given that Mr. Erdogan appeared to have a near-monopoly on power. Only two months ago, Mr. Erdemir said, he wrote an article declaring that the era of the coup d’état in Turkey was over.  “It is extremely surprising,” he said, “because no one would’ve believed there was a group of officers with the audacity to try and take on Erdogan.”  Eric Schmitt reported from Washington, and Dan Bilefsky from London.  A version of this article appears in print on July 17, 2016, on page A11 of the New York edition with the headline: Authorities Interrupt Missions Against ISIS at a Major Air Base. Order Reprints| Today's Paper|Subscribe
A Pentagon spokesman said United States officials were “working with the Turks to resume air operations there as soon as possible.”