Obama called on Iran to "immediately release Saeed Abedini, Amir Hekmati and Jason Rezaian" and to "work cooperatively" to find Robert Levinson "so that they all can be safely reunited with their families as soon as possible."
The message was timed to coincide with Nowruz, Iran's New Year holiday.
The US and Iran have long been foes. Diplomatic ties were snapped in the wake of the 1979 Iranian Revolution and the subsequent hostage crisis in Tehran, when US diplomats were held hostage by militant students for 444 days.
Obama recently met the wife of Abedini, a Christian pastor who has been jailed in Iran for more than two years, vowing to work to win his release.
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Former US Marine Hekmati and Washington Post journalist Rezaian are also in detention in Iran.
Levinson disappeared on March 9, 2007 during a visit to the Iranian island of Kish.
The 67-year-old Levinson retired from the Federal Bureau of Investigation 17 years ago.
The US government has denied Levinson was working for the US government when he vanished, but news reports have suggested the CIA had been paying him to gather intelligence.
Obama's appeals comes after a video message Thursday in which he urged Iran's people to grasp a "historic" chance to transform long-frayed ties.
The ongoing talks on Iran's nuclear program, he said, presented "the best opportunity in decades" to improve relations.