The Iranian response was sent via Pakistan on Sunday, state media said.
President Donald Trump announced "major combat operations" against Iran on Feb. 28, with massive joint U.S.-Israeli strikes targeting military, government and infrastructure sites.
Following the announcement of a two-week ceasefire, initial U.S.-Iran talks in Pakistan in April failed to reach a peace deal.
Trump later announced the open-ended extension of the ceasefire and the continuation of a U.S. blockade until negotiations are concluded "one way or the other."
As the U.S. awaits Iran’s response to its peace proposal, President Donald Trump said Saturday that he "expects to hear very soon" from the Iranians, according to French news outlet TF1 Info.
In an interview, Trump also told the outlet "they still very much want to conclude a deal."
President Donald Trump told reporters he was expecting to receive a response on a peace plan from Iran on Friday night but said, "We'll see what happens."
Trump made his remarks as he left the White House on Friday evening.
Asked if the U.S. had received a response from Iran, Trump said: "We're receiving a letter, supposedly tonight, but we'll see how that goes."
Trump was pressed on Iranian attacks that have persisted in Kurdish areas of Iraq amid the ceasefire, with the president saying that he was focused on getting the entire conflict in the Middle East ended.
"We want to get the whole thing ended, and we will," he said.
-ABC News' Nicholas Kerr and Michelle Stoddard
The Treasury Department announced sanctions targeting 10 individuals and companies it claims are "enabling efforts by Iran's military to secure weapons" and providing raw materials for its drone and ballistic missile program.
The individuals and companies are based across the Middle East, Asia and Eastern Europe, the department said.
"Under President Trump's decisive leadership, we will continue to act to Keep America Safe and target foreign individuals and companies providing Iran's military with weapons for use against U.S. forces," Treasury Secretary Scott Bessent said in a statement.
During the U.S.-Israeli strikes at the beginning of the war, Iran's supreme leader, Mojtaba Khamenei, was injured by a blast wave and suffered injuries to his kneecap, back and the area behind his ear, an Iranian official revealed during a state gathering on Friday, according to the semi-official Tasnim News Agency.
This marks the first time an Iranian official has detailed the injuries sustained by the new leader of the Islamic Republic during the opening strikes.
The official -- Mazaher Hosseini, head of visits at the office of the late Islamic Republic Supreme Leader Ali Khamenei -- said that Mojtaba Khamenei was going up the stairs at the time and was thrown to the ground by the blast wave.
He has recovered from his back injury and his kneecap is expected to heal soon, Hosseini said, adding that the leader is in "perfect health."
-ABC News' Somayeh Malekian
