The Persian Gulf Strait Authority (PGSA), a newly created Iranian government agency responsible for maritime traffic in the Strait of Hormuz, appeared to reject U.S. President Donald Trump's claim that the U.S. fully controls the vital waterway.

"Claims and repeated posts by U.S. officials that the Strait of Hormuz is no longer blocked do not change the reality: the Strait of Hormuz remains blocked and will not be reopened until Iran’s conditions are accepted," the PGSA wrote in a social media post Wednesday evening.

-ABC News' Morgan Winsor

President Donald Trump said the U.S. has "total control" of the Strait of Hormuz and then hinted that he wants the U.S. to "KEEP" the key waterway, in a social media post Wednesday.

"The U.S.A. has total control over the Strait of Hormuz. I THINK WE WILL KEEP IT!" Trump said in the post.

The president then touted the success of the U.S. naval blockade and repeated his claim that Iran's military capabilities have been diminished.

"They have No Money - Their country is 'shot.' All they have is FAKE NEWS and 300% INFLATION, and getting worse," Trump said.

"Iran is all talk and no action, the Bully of the Middle East No Longer," Trump said.

International Maritime Organization Secretary-General Arsenio Dominguez released a statement on Wednesday condemning Tuesday's deadly attack on a cargo ship off the coast of Yemen.

At least six people were killed in two attacks on the Egyptian-owned Tihamah cargo ship on Tuesday, Yemeni officials said.

"It is particularly troublesome that the most recent attack has taken place in the Red Sea and Gulf of Aden area," Dominguez said. "I reiterate my call for shipowners and ship operators to thoroughly assess risks before transiting this and other regions and follow appropriate best management practices."

"These continued attacks on shipping only serve to escalate tensions and threaten global supply chains on which everyone depends," he added.

The Iran-aligned Houthi rebels in Yemen said that they targeted "a Saudi military equipment transport ship" in the area, though did not name the vessel.

While gaggling with reporters at Joint Base Andrews on Tuesday evening, President Donald Trump said the situation in Iran is progressing "absolutely fine," again insisting that the U.S. has total control over the Strait of Hormuz.

"Iran is going fine, going just absolutely fine. We totally control the Strait of Hormuz. We have control over it. Nobody else, only us. Our navy is unbelievable, and things are going great for our country," he said.

Despite the president's insistence that talks are going well with Iran, he made clear that he does not trust Tehran's representatives and that renewed military action is still possible.

"I don't trust Iran," Trump said. "I'm the last person to trust Iran. They've lied to me constantly. We have total control over the Hormuz Strait right now. They don't have control. We have total control. We own it."

"And at some point, maybe they'll do something and then they get blown away," Trump added. "Right now, we're in a very good position."

-ABC News' Emily Chang, Devin Garbitt and Nicholas Kerr