Iran live updates: 'Time is not my adversary,' Trump says on securing deal

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

As the Iran conflict drags on, President Donald Trump insists that he is not facing any time constraints to secure a deal, pushing back on reports that say he is under "pressure."

"I am under no pressure whatsoever, although, it will all happen, relatively quickly! Time is not my adversary," Trump wrote on social media.

The president insisted that he is ahead of schedule militarily.

"They like to say that I promised 6 weeks to defeat Iran, and actually, from the Military standpoint, it was far faster than that, but I'm not going to let them rush the United States into making a Deal that is not as good as it could have been," Trump wrote.