In a statement, the outspoken Iran critic sent "best wishes to all those around the world celebrating the wonderful ancient holiday of Nowruz."
This year Persian New Year, or Nowruz, falls on Tuesday, March 21.
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President Barack Obama issued such well wishes every year, in a bid to break through to Iranians skeptical about US intentions.
The US and Iranian governments still have no formal diplomatic relations, despite a recent deal that saw Iran curb its nuclear program in exchange for sanctions relief.
The government in Iran often whips up anti-US sentiment, something that Trump has appeared willing to reciprocate.
In its early days in office Trump's administration put Iran "on notice" that the US would take a tougher line against Iranian actions across the Middle East.