President Donald Trump has suggested that the Strait of Hormuz will be "OPEN TO ALL" should Iran agree to U.S. demands, as hopes have grown that a deal to end the Middle East conflict may be edging closer.

In a social media post, Trump said that the U.S. assault on Iran, which Washington began with Israel in late February, "will be at an end" if Tehran "agrees to give what has been agreed to."

Trump did not elaborate further on what promises Iran had made, but threatened to resume bombardments "at a much higher level and intensity than it was before" should a deal fall through. He has claimed that "great progress" has been made in reaching an accord.

But the president told the New York Post that it was "too soon" to start thinking about possible in-person discussions with Iran.

Meanwhile, an Axios report said the White House believes that it is nearing a deal with Iran on a one-page memorandum of understanding to end the war, adding that the document would lay out a framework for more detailed nuclear negotiations.

Washington expects Tehran to respond on several major points within the next 48 hours, the report said. While nothing has yet to be agreed, this was the closest both sides have come to concluding the conflict since the outbreak of the fighting in late February, Axios said.

A potential deal would see Iran commit to a moratorium on nuclear enrichment, while the U.S. would agree to remove sanctions and release billions of dollars in currently frozen Iranian funds. Restrictions on the Strait of Hormuz would also be lifted to once again allow transit through the chokepoint, Axios reported.

An Iranian foreign ministry spokesperson said they were "evaluating" Washington’s proposal, CNBC reported. Pakistan, which has served as a mediator between the U.S. and Iran, also confirmed that both sides are closing in on an agreement, Reuters added.

Iran has indicated that it will only accept a "fair and comprehensive agreement" in talks with the U.S. to conclude the war, Tehran’s foreign minister said. Speaking in China following a meeting with Beijing’s top diplomat, Iranian Foreign Minister Abbas Araghchi added: "We will do our best to protect our legitimate rights and interests in the negotiations."

Notably, Beijing is a key buyer of Iranian oil, and media reports have suggested that China could be looking to persuade Tehran not to escalate tensions with the U.S. ahead of a meeting between Chinese leader Xi Jinping and Trump next week.

Oil prices retreated on Wednesday, with Brent crude futures, the global oil benchmark, last oscillating around $100 a barrel. Still, the Brent contract is well above pre-war levels of roughly $70 a barrel. Global financial markets rallied and U.S. stock futures rose as well.

Trump pauses "Project Freedom"

Earlier, Iran’s paramilitary Revolutionary Guards Navy reportedly said that safe and stable transit of the Strait of Hormuz will be possible. Citing Iranian state media, Reuters reported that the comment came after what the Revolutionary Guards described as the end of "threats from aggressors."

Trump announced on Tuesday that so-called "Project Freedom," a U.S. push to unblock the Strait of Hormuz by using military force to guide ships through the narrow the waterway, was being halted "for a short period of time."

The drive, which came into effect earlier this week, was soon followed by a fresh bout of attacks in the strait and the Gulf region, including on sites in the United Arab Emirates. Trump said that the change had come at the request of Pakistan and other countries.

The Strait of Hormuz, a major conduit for a fifth of the world’s oil, remains effectively closed off to tanker traffic, as it has for weeks. Both the U.S. and Iran have set up blockades.

An energy shock caused by continued disruptions to shipping activity in the strait has contributed to fears over a spike in inflation around the world and a slowdown in global growth.