“This is clearly a setback for the ideology that Qatar and Turkey support and encourage,” said one Arab official, who spoke on the condition of anonymity so as not to antagonize two powerful nations. “If political Islam was a stock, it would have gone down dramatically over the past week.”

Qatari officials declined to comment on the rivalry. But one Qatari official, speaking on condition of anonymity, said Qatar’s financial aid in the past had been to the Egyptian people, not any individual figure or party.

The Qataris suffered two other, lesser setbacks in recent days: on Monday, 22 journalists at Al Jazeera resigned en masse, citing what they said was the station’s biased coverage of the Brotherhood. Al Jazeera’s bias in favor of the Islamist group has often been cited as a grievance against Qatar’s rulers, who are accused of using the station as an arm of their activist foreign policy.

Also on Tuesday, Ghassan Hitto, the prime minister of the main Syrian exile opposition group — who was seen as favorable to Qatar — resigned. Although the reasons for his resignation were not clear, it was generally viewed as a concession to Saudi Arabia, which had signaled its discontent with him.

Some analysts say Qatar has already begun to rein in its aggressive and eclectic foreign policy, which has included a willingness to engage with Iran that infuriated its Saudi neighbors. Last week, Qatar’s government joined Saudi Arabia and others in issuing a message of support to the transitional government installed by the Egyptian military, even as its allies in the Brotherhood protested furiously against what they called a military coup.

“It’s starting to look as if the Qataris have ceased playing the role of troublemaker and freelancer in the region, and falling in behind the Saudis,” said Peter Harling, an adviser with the International Crisis Group. “Events are allowing the Saudis to assume a regional leadership role that no one else can play right now.”

Despite Qatar’s strong financial support for Mr. Morsi’s government, some analysts say Qatari officials had privately become very critical of his many blunders over the past year. “The Qataris were not happy with the decision to take Morsi out, but they were not so happy with Morsi, either,” said Mustafa Alani, an analyst with the Dubai-based Gulf Research Center.