A White House spokesman said Michael White's release may lead to an opening in the otherwise deeply bitter relationship between Iran and the United States.
While the virus has struck both countries, killing thousands of people, they continue to target each other on foreign battlegrounds.
The US alleges Iran's satellite programme is a cover for its development of missiles, while the Islamic republic has previously insisted its aerospace activities comply with its international obligations.
It was not immediately clear what information Trump was referring to in his tweet, which was posted after he was scheduled to have an intelligence briefing.
The US strikes that target Shia militias actually target a branch of the Iraqi Army.
The disqualification of some 9,000 potential candidates, most of them reformists and moderates, raised the possibility of lower-than-usual turnout.
"It was launched with success and ... we have reached most [of] our aims ... but the "Zafar" satellite did not reach orbit as planned," a top defence ministry official says.
Mohammed Allawi represents the same establishment protesters want to get rid of, and this is best encapsulated by Moqtada al Sadr's u-turn on the protest movement.
Iran's Technology Minister Mohammad Javad Azari-Jahromi says the "Zafar satellite" will be launched by the end of this week, a programme the US sees as camouflage for Tehran's missile development.
Out of 50 US service members diagnosed with traumatic brain injuries, 31 were treated in Iraq and returned to duty, says Pentagon official
The march called by prominent Shia cleric Muqtada al Sadr aims to pressure Washington to pull out its troops.
The most outspoken celebratory messages for the killing of the controversial Iranian general came from the Turkey-backed Syrian National Amy, while the YPG-dominated Syrian Democratic Forces remain silent.
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