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During their conversation Wednesday morning, Mrs. Sweeney asked her son whether he had participated in the protests.

“I said, ‘Did you throw anything off a roof?’ And he said ‘No, I didn’t,’” she told reporters earlier this week. “And then I said, ‘Did you do anything else?’ He said, ‘No, none of us did.’”

Mrs. Sweeney also said her family has been assured that Egyptian officials will not appeal the judge’s decision.

Mr. Sweeney, Mr. Gates and Mr. Porter are expected to be taken first to a Cairo police station to fill out paperwork, then return to their dorm rooms and gather up personal belongings, though it is unclear how soon they will leave the country.

They remained in custody late Thursday.

The ongoing violence has, according to al-Jazeera television, also led Egyptian authorities to postpone elections set to begin Monday, the first free election in decades.

Many protesters doubt the Egyptian army’s ability to oversee a fair vote, but the junta quickly denied the delay reports.

“There will be no postponement in the election,” said Maj. Gen. Mamdouh Shaheen, a member of the ruling military council said on Egyptian TV on Thursday.

“The election will be held on time with all of its three stages on schedule.”