Analysts said the reality was more complicated. “The Qataris made a better grade on counterterrorism and the Saudis overplayed their hand,” said Aaron David Miller of the Wilson Center, a former negotiator and Middle East analyst for the State Department. “And the combination of those two things meant we have restored balance in our relationships in the Gulf.”

Mr. Tillerson heads to the Middle East next week, where the growing American tilt toward Qatar is likely to be on stark display. At a meeting in Kuwait to solicit investments and donations for Iraq’s reconstruction, the Qataris are expected to make a significant pledge of funds, according to a senior State Department official. But the Saudis, saddled with a costly war in Yemen, and Emiratis, long suspicious of Iraq’s Shiite-led government, are not expected to make similar pledges, said diplomats in the region who spoke on the condition of anonymity because the funding assistance had not yet been announced.

Qatar’s foreign minister and defense minister led the delegation to Washington last week for the country’s first strategic dialogue with the United States — a diplomatic platform that the Trump administration has generally reserved for global heavyweights like China and India. Mr. Tillerson has been among Qatar’s chief supporters in the administration; he played a key role when he was at Exxon Mobile helping Qatar develop its vast gas field.

There are signs that Mr. Tillerson’s view now holds sway in the White House.

Since the summer, the Trump administration has become increasingly unnerved by Saudi moves to remove Lebanon’s prime minister, jail hundreds of princes and businessmen and prosecute a war in Yemen that has created a humanitarian disaster. Additionally, Stephen K. Bannon, Mr. Trump’s one-time chief strategist who has close ties to the Emirates and has sharply criticized Qatar, is no longer at the White House.

Qatar, meanwhile, signed agreements with the United States for sharing information on terrorists and terrorist financing, fighting human trafficking and disclosing detailed financial information about its national airline. Last month, Mr. Trump called Emir Tamim bin Hamad Al Thani of Qatar and praised the nation for being “one of the few countries” to sign a counterterrorism agreement.