The ceasefire announced earlier this month was set to expire on April 22.
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 earlier this month failed to reach a peace deal. On Tuesday, Trump announced he is extending the ceasefire and continuing the blockade until Iran's proposal is submitted and discussions are concluded "one way or the other."
Iranian Ambassador to Pakistan Reza Amiri Moghadam said in a post to X on Tuesday that Iran "will Not negotiate under Threat and Force," as U.S. and Iranian representatives prepared to meet for a new round of expected peace talks in Islamabad.
Speaking to Fox News Monday evening, White House Press Secretary Karoline Leavitt said the U.S. and Iran are on the "brink" of securing a deal, though she did not provide any insight into the state of potential peace talks.
"The United States of America tonight have never been so close to making a truly good deal," she said.
This comes despite Speaker of the Iranian Parliament Mohammad Bagher Ghalibaf issuing a new statement Monday: "We do not accept negotiations under the shadow of threats, and in the past two weeks, we have prepared to reveal new cards on the battlefield."
Leavitt also praised President Donald Trump's "hard-line negotiating style," something she has previously credited for bringing Iran to the table.
"Thanks to the success of the military operation and his hard-line negotiating style, we are on the brink of a deal. If not, the president as commander in chief still has a number of options at his disposal he is not afraid to use, President Trump has proven before he does not bluff," Leavitt said.
-ABC News' Emily Chang
President Donald Trump wrote on social media that the U.S. naval blockade in the Strait of Hormuz will not be lifted until the U.S. and Iran reach a deal.
"(This has been, in addition to everything else, Regime Change!), and perhaps, most important of all, THE BLOCKADE, which we will not take off until there is a "DEAL," is absolutely destroying Iran," Trump wrote.
In a separate post, the president claimed that the closure of the Strait of Hormuz has "forced" other countries to come to the U.S. for oil.
"The Iranian leadership has forced hundreds of Ships toward the United States, mostly Texas, Louisiana, and Alaska, to get their Oil -- Thank you very much!" he wrote.
At least 415 U.S. troops have been wounded in the war with Iran, according to Defense Department data.
Last week, the total stood at 399. The rise during the ceasefire is tied to delayed reporting of injuries, especially traumatic brain injuries, in which symptoms can emerge or be recognized days later.
-ABC News' Steven Beynon
