An agency official told members of Congress on Monday that leaders in local offices had been “asked to remain vigilant and increase their situational awareness given the evolving threat environment.”

A half-dozen people of Iranian descent who were held for additional questioning in Washington described extensive questioning about their family and background, even though, like Ms. Hekmati, many were American citizens. One woman said she was asked to write down the name of the high school she graduated from in Iran 39 years ago. Another person was asked about his parents’ military service from before the 1979 Iranian Revolution. Others were asked to identify details about their Facebook accounts.

Representative Pramila Jayapal, Democrat of Washington, said she had heard that as many as 200 people of Iranian descent may have been affected.

Legal advocates at a Monday news conference in Seattle described several cases of travelers being questioned about their feelings about the United States and what was happening in Iran.

“United States citizens and legal permanent residents do not have to answer questions about their political views or religious views and practices, and cannot be denied entry into the United States for declining to answer these questions,” said Hina Shamsi, director of the American Civil Liberties Union’s National Security Project.

Ms. Shamsi said some of the questioning appeared to violate First Amendment rights. Under the law, she said, border agents who question citizens and legal permanent residents are permitted to verify only identity, legal status and whether a person is carrying contraband.

But she said the A.C.L.U. had for years tracked cases of invasive and sometimes unlawful questioning by border officers that went beyond those limits, into political and religious views and practices. She said she had seen such questions directed at Americans of Somali, Afghani and Pakistani backgrounds following military action in those countries.