During an appearance in New York Friday, President Donald Trump claimed when the conflict with Iran concludes, he'll make the Strait of Hormuz territory of the United States.

"And after we finish defeating Iran, which is being very badly defeated, pretty soon I'll be declaring the Hormuz Strait a territory of the United States," the president said.

The U.S. has no formal jurisdiction over the strait. The president did not share more details about the claim.

President Trump maintains that the U.S. controls the waterway and is winning against Iran, while the Iranians maintain that they are managing the strait and demand the lifting of the U.S.' blockade in order to open it.

Iranian officials responded on Friday, saying the strait was and would remain under Iranian control.

"The Strait of Hormuz cannot be seized by tweet, nor by aircraft carrier, nor by issuing an order, nor by an election speech. Iran neither fears threats nor cowers before displays of power," said Kazem Gharibabadi, Iran's Deputy Foreign Minister for Legal and International Affairs.

RELATED STORY | US prepared to hold Strait of Hormuz 'indefinitely', Hegseth says

Treasury Secretary Scott Bessent in an interview with Newsmax this week suggested there could be significant new economic measures against Iran to come, while Defense Secretary Pete Hegseth suggested the U.S. could continue the naval blockade as long as needed.

A U.S. official who spoke to Scripps News pointed out the president's preference for a diplomatic solution, but also said that President Trump "continues to retain all options if Iran continues to engage in terrorism and refuses to make a deal."