Pastor Abedini was sentenced to 8 years in an Iranian prison for "attempting to sway Iranian youth away from Islam" and creating house churches. He has been detained since 2012.
The resolution also calls on Iran to release Washington Post journalist Jason Rezaian, former marine Amir Hekmati and former FBI agent Robert Levinson.
Senate Majority Leader Mitch McConnell said the Pastor, who converted to Christianity in 2000, had been, "Beaten, denied access to medical care, and locked away in solitary confinement".
McConnell called on the Obama administration to "use the tools it has in pursuit of what should be a bipartisan goal: securing the release of American citizens being held as hostages by the regime in Iran."
He said: "No American should find this acceptable. Just as no American should find it acceptable to unjustly imprison a reporter, or a grandson coming to see his grandmother. I think we can all agree that, at the very least, the American government should not be rewarding Iran for its disgraceful human-rights abuses - that we should not be granting Iran access to the funding it desires to further its nuclear weapons program and terrorist proxies while this exploitation continues."
Pastor Abedini's family say they fear for the continuous threat to his life from fellow inmates and are worried about his deteriorating health, as he has been repeatedly denied medical attention for the injuries he sustained from the beatings of inmates and prison authorities.
Senetor Jim Risch of Idaho, who presented the resolution said, "It is only right that the president should ensure Iran frees Pastor Abedini and the other Americans they have held captive for too many years before the United States provides any sanctions relief."