"I said I hope you're going to negotiate, because it's going to be a lot better for Iran," Trump said in the interview with Fox Business Network broadcast Friday.
"I think they want to get that letter. The other alternative is we have to do something, because you can't let another nuclear weapon."
There was no immediate response from the foreign ministry in Iran, where it is currently the weekend, to a request for comment on Trump's remarks.
The letter appeared to have been addressed to Iran's Supreme Leader Ayatollah Ali Khamenei. The White House did not immediately respond to a request about that.
"There are two ways Iran can be handled: militarily, or you make a deal," Trump said. "I would prefer to make a deal, because I'm not looking to hurt Iran. They're great people."
Trump has upended U.S. foreign policy after taking office in January, adopting a more conciliatory stance towards Russia that has left Western allies wary as he tries to broker an end to Moscow's three-year-old war in Ukraine.
He said in February he would like to make a deal with Iran that prevents that country from developing a nuclear weapon.
Russian Deputy Foreign Minister Sergei Ryabkov discussed international efforts to resolve the situation around Iran's nuclear program with Iranian ambassador Kazem Jalali, the Russian Foreign Ministry said on Friday.
