Iran had received a letter from Vance but it has not responded to it yet, Iranian news agency Tasnim reported on Thursday.
Vance sent the letter to Iranian Security Council chief Mohsen Rezaei in a bid to revive peace negotiations, the Wall Street Journal and the New York Times reported on Wednesday, citing US officials and people familiar with the matter.
The Wall Street Journal reported that Vance sent the letter at Trump's direction.
When asked by reporters later on Wednesday if he directed Vance to reach out to Iran to restart peace negotiations, Trump said: "No."
"What that is is they need help with medical supplies and various things. He (Vance) asked me what I thought. I said, if you want to do that, that's okay. Basically, it's getting supplies in to help people that are not well," Trump told reporters.
Iran's mission to the United Nations in New York did not immediately respond to a request for comment on the letter and Trump's remark. Vance's office did not immediately respond to a request for comment.
The United States and Israel launched a war against Iran at the end of February.
The US has also since imposed a naval blockade on Iran to starve it of oil export revenue and escalated efforts to economically isolate Iran.
Iran has long blamed US sanctions for hindering civilian access to medical supplies.
In an August letter to the United Nations Security Council, Iran accused the US of intentionally depriving civilians "of access to food, medicines, medical equipment, energy and other necessities, with grave consequences for their rights to life, health, food and a decent standard of living".
Qatari mediators presented Iran with a new draft deal on Sunday to end the war but a senior Iranian official said Qatar had only put forward unacceptable ideas that did not amount to an offer.
The war's effect on global energy costs has also weighed on support for Republican candidates and hurt Trump's approval ratings ahead of the US midterm elections that decide control of Congress.
