CAIRO — For a moment, at least, American and European diplomats trying to defuse the volatile standoff in Egypt thought they had a breakthrough.

As thousands of Islamist supporters of the ousted president, Mohamed Morsi, braced for a crackdown by the military-imposed government, a senior European diplomat, Bernardino León, told the Islamists of “indications” from the leadership that within hours it would free two imprisoned opposition leaders. In turn, the Islamists had agreed to reduce the size of two protest camps by about half.

An hour passed, and nothing happened. Another hour passed, and still no one had been released.

The Americans heightened the pressure. Two senators visiting Cairo, John McCain of Arizona and Lindsey Graham of South Carolina, met with Gen. Abdul-Fattah el-Sisi, the officer who ousted Mr. Morsi and appointed the new government, and the interim prime minister, Hazem el-Beblawi, and pushed for the release of the two prisoners. But the Egyptians brushed them off.

“You could tell people were itching for a fight,” Mr. Graham recalled in an interview. “The prime minister was a disaster. He kept preaching to me: ‘You can’t negotiate with these people. They’ve got to get out of the streets and respect the rule of law.’ I said: ‘Mr. Prime Minister, it’s pretty hard for you to lecture anyone on the rule of law. How many votes did you get? Oh, yeah, you didn’t have an election.’ ”