Secretary of State Clinton calls on Tehran to "do the right thing" and release them.
Various Iranian officials have suggested they intended to carry out acts of espionage against Iran but no charges have been filed against them despite intensive interrogation.
At a news briefing, State Department Spokesman P.J. Crowley read a statement by Secretary Clinton on what he termed a "tragic" anniversary.
"Their release by the Iranian government is long overdue," he said. "Their continued detention is unjustifiable. Iran has long espoused to the world its commitment to justice, security and peace for all. We urge Iran to take action on the three hikers detained for a year in Evin prison without charge to match these stated commitments. We call on Iran to do the right thing and allow these three Americans to return home to their families."
Amnesty International-USA, in its statement on the anniversary, said it appears clear that Iranian authorities do not have substantial grounds to prosecute the three Americans, and that they may be held solely because of their nationality.
The human rights group's Middle East director, Malcolm Smart, cited statements by Iranian leaders including President Mahmoud Ahmadinejad suggesting the three are being held to pressure the U.S. government for diplomatic concessions.
He said if that is the case, their detention would amount to hostage-taking and be a very serious abuse of human rights.
Swiss embassy officials who represent U.S. interests in Tehran have not been allowed to visit the three since April. But in late May they were taken to a Tehran hotel and allowed to meet their mothers who had traveled from the United States.
Last month, the U.S. news magazine The Nation said an investigation by its reporters turned up two Iraqi Kurdish witnesses who said Iranian police crossed several yards into Iraq to seize the hikers after they ignored shouted demands and a warning shot to enter Iran.
One of the Americans, Shane Bauer, also was heard denying walking into Iran during a brief film clip of his Tehran reunion with his mother on May 20.
In its repeated calls for the release of the hikers, the State Department has also appealed to Iran to provide information on the whereabouts of Robert Levinson. The former agent of the U.S. Federal Bureau of Investigation disappeared shortly after arriving at an Iranian island resort in 2007.