“People can freely vent their frustrations and go to the polls to vote,” he added.

For some members of Congress, the latest developments are nonetheless disturbing. Representative Peter T. King, a New York Republican and chairman of the Homeland Security Committee, said Mr. Morsi’s call for the release of Omar Abdel Rahman, a blind Egyptian sheik who is serving a life term, was “the kind of talk you hear on the street — not from the president of the country.”

“We have to be concerned,” Mr. King added.

He wrote to Janet Napolitano, the secretary of homeland security, demanding an explanation for Mr. Eldin’s visa. “If we’re going to allow someone from a notorious terrorist group into the country, it should be the result of a long, public process of decision-making,” Mr. King said.

There are historical precedents, Mr. King acknowledged, citing one he knows intimately. A longtime supporter of the Irish Republican Army, Mr. King lobbied for years for a visa for Gerry Adams, head of what was the I.R.A.’s political wing, Sinn Fein, before it was granted in 1994.

“But that took years of negotiation, and it was done openly,” Mr. King said, by contrast with the visit by Mr. Eldin, which was not known about publicly until it was reported by The Daily Beast.

An earlier precedent might be the Zionist militants who took part in terrorist acts against the British before the creation of the State of Israel, then became leading politicians who were warmly welcomed in Washington.

Gamaa al-Islamiyya appears to be another case of a terrorist organization gradually changing its tactics. The group carried out a brutal campaign of violence in the 1990s, killing Egyptian soldiers and police officers and foreign tourists. But it renounced violence in 2003, and since then has sought to enter the political mainstream.

The sheik, 74, now in a federal prison for ailing convicts at Butner, N.C., was a leading figure in the group during its violent days. He was sentenced in 1996 for plotting a “war of urban terrorism” against the United States, beginning with the bombings of tunnels and landmarks in New York City.