US President Donald Trump said Sunday that the US-Iran peace deal "is now complete" and he has authorized the toll-free opening of the Strait of Hormuz and the immediate removal of the US naval blockade against Iranian ports, according to Xinhua.

"The Deal with the Islamic Republic of Iran is now complete," Trump wrote on his Truth Social. "I hereby fully authorize the toll free opening of the Strait of Hormuz, and, simultaneously herewith, authorize the immediate removal of the United States Naval blockade."

"Ships of the World, start your engines. Let the oil flow!" said Trump.

The agreement would be signed electronically by him or by Vice President JD Vance in person, Trump told The Wall Street Journal in an interview hours earlier.

The deal would include a commitment from Iran not to obtain nuclear weapons and an immediate reopening of the Strait of Hormuz, Trump told the newspaper.

He also expressed no urgency to extract nuclear material from Iran, saying "there's no rush."

"We'll get the nuclear dust later on when we're ready to go in and do it. I'd say over the next month or two, there's no rush," he said.

There would be strong nuclear inspections on the Iranians, Trump said, without specifying how they would work.

Under the deal, Iran wouldn't be provided cash but sanctions could potentially be lifted, Trump added.

"We'll see how they behave," he said.

Not long before Trump's post on the deal, Pakistani Prime Minister Shehbaz Sharif announced on X that an official signing ceremony of the deal is scheduled for June 19 in Switzerland.

Meanwhile, Iranian Deputy Foreign Minister for Legal and International Affairs Kazem Gharibabadi said early Monday that the US naval blockade against Iran will be lifted as of tonight and the immediate and permanent end of the war and military operations on all fronts, including Lebanon, is announced, Xinhua reported. 

Gharibabadi said Iran and the United States will sign the finalized draft of a peace memorandum of understanding (MoU) in Switzerland on June 19, according to Iran's semi-official Tasnim news agency.

Tasnim also cited a source as saying that the Strait of Hormuz will reopen following the signing ceremony in Switzerland.

Meanwhile, Iran's state-run IRIB TV, also citing Gharibabadi, said Iran's entry into a 60-day period of negotiations with the United States on its nuclear program and the removal of sanctions will hinge on the US fulfillment of its preliminary commitments, which will be verified by Tehran from now until the signing ceremony.