Washington CNN  — 

The families of four Americans imprisoned or missing in Iran went to Capitol Hill on Tuesday to plead for the safe return of their loved ones, just as negotiators seek to expand ties with the longtime U.S. foe through a historic nuclear agreement.

Speaking to lawmakers at a House Foreign Affairs Committee hearing, Sarah Hekmati, whose brother Amir, a former U.S. Marine, was sentenced to 10 years in prison for “practical collaboration with the U.S. government,” said her family “has been living a nightmare” for more than three years.

“We are in constant fear for his health, his safety and his life,” she said.

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Hekmati was joined by Ali Rezaian, brother of detained Washington Post reporter Jason Rezaian; Nagameh Abedini, wife of detained pastor Saeed Abedini; and Daniel Levinson, whose father, Bob Levinson, has been missing in Iran since 2007.

“We believe that if the Iranian government had the will and motivation to locate my father and send him home, they most certainly could,” the younger Levinson said. “My family will never rest until our father is back home with us.”

Iranian officials have denied any knowledge of Levinson’s whereabouts.

“He was still a contractor for the U.S. government at the time of his capture,” Daniel Levinson said of his father, a former FBI agent and contractor for the CIA. “Therefore, the U.S. has a moral obligation to help bring him home.”

Members of Congress on both sides of the aisle voiced outrage over Iran’s continued detention of these Americans and urged the Obama administration to demand their release.

“We must make it clear, in no uncertain terms, that we will not allow the regime to hold American citizens and deny them their due process while torturing them and subjecting them to inhumane treatment,” said Florida Republican Rep. Ileana Ros-Lehtinen.

“It would just be ludicrous and outrageous for us to have a deal with Iran that doesn’t include the bringing home of our hostages,” said Rep. Eliot Engel, D-New York, the committee’s top Democrat.

U.S. officials say they raise these cases with their Iranian counterparts frequently on the sidelines of the nuclear talks, but Nagameh Abedini said that hasn’t been enough.

“I appreciate that they’re being discussed on the sidelines, but they’re still not home,” she said. “Where’s the action? Where’s the result?”

A State Department official said on Tuesday the administration has “long called for these U.S. citizens to be released and returned home.”

“We remain engaged at the highest level on these cases,” the official said. “The only other issue Secretary Kerry and Under Secretary Sherman discuss every time they meet with their Iranian counterparts, other than the nuclear negotiations, are the cases of these four Americans.”

The U.S. and five other world powers have been in talks with Iran on the nuclear issue since 2013, and are approaching a June 30 deadline to reach a comprehensive agreement.

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If reached, that deal would give Iran relief from crippling international sanctions in exchange for a rolling back of its nuclear program.

But the State Department official said the U.S. also doesn’t believe the hostage cases should be tied to the outcome of the talks.

“As we’ve said again and again, these cases should be resolved whether or not we can reach a successful outcome to the nuclear talks,” the official said. “So we will continue to press for their release regardless of what happens with the nuclear talks over the next month.”

Several lawmakers became emotional during the hearing, including North Carolina Republican Rep. Mark Meadows, who seemed to tear up as he compared the current detentions to the Iranian hostage crisis.

“In the late seventies there were thugs and terrorists that took hostages, and they wore ski masks and dark clothing,” he said. “And the only difference today is that the terrorists and thugs wear suits and give the illusion of being international diplomats, and that is not the case.”

CNN’s Jim Sciutto and Jennifer Rizzo contributed to this report.