President Donald Trump on Wednesday physically signed the memorandum of understanding between the U.S. and Iran that ends the war, a White House official confirmed.

"On Sunday, the MOU was signed digitally by Vice President Vance and Speaker Ghalibaf and witnessed by President Trump. Now, it has been signed by President Trump and President Pezeshkian," a White House official said in a statement shared with ABC News.

A White House official, along with another source familiar, says this signing occurred during Trump's dinner with French President Emmanuel Macron at the Palace of Versailles on Wednesday.

A photo of the signed document was sent to Iran and mediating countries, according to a source familiar with the matter.

With Trump's signing, the agreement is "now in effect," a White House official confirmed -- which would mean that the Strait of Hormuz could open.

The White House did not immediately answer ABC News when asked whether the strait is now open.

-ABC News' Chris Boccia and Isabella Murray

After the details of the memorandum of understanding were verbally released by senior administration officials, Democratic Senate Minority Leader Chuck Schumer said the war in Iran "will be regarded as one of the biggest American disasters."

Trump "started this war, he didn't know how to finish it, and it looks like in too many ways he has just capitulated to the Iranians," Schumer told reporters outside the Capitol.

"When you look at the 14 points that the administration has agreed to, it looks like Iran has won on just about every one of them. Trump has done a very poor job of negotiating. We are worse off than we were when the war started," Schumer added.

-ABC News' Lalee Ibssa

Iran's foreign ministry spokesperson Esmail Baghaei said the memorandum of understanding has been "finalized" and will be digitally signed by the presidents of Iran and the U.S., in comments carried by state media.

Baghaei said Iran plans to charge fees for the Strait of Hormuz and that a plan for managing the waterway has been "largely finalized with Oman."

In a statement carried by the Fars News agency, Baghaei said that the 60-day negotiating period is "reasonable" and could be extended if necessary, and said Iran plans to negotiate "on the nuclear issue and sanctions."

He said transferring enriched nuclear material out of Iran "is unacceptable to us."

He also highlighted the inclusion of Lebanon, saying the ceasefire and the end of the war there "are as important as for Iran."

President Donald Trump said the 60-day negotiating period is not a hard deadline for Iran, and that it could possibly take longer.

"Just as long as they're behaving, I really don't care that much," Trump told reporters shortly after touching down in Paris.

Trump was asked to clarify his comments about allowing Iran to have ballistic missiles, to which he doubled down and said, "if other countries have them, it's a little bit unfair for [Iran] not to have some.”

"A ballistic missile is not the same thing as what we're talking about when we talk nuclear, but if Saudi Arabia and Qatar, and they all have some, I would say in relative proportion, I think it's okay. That’s what I mean," Trump said.

Asked how long the U.S. military will remain in the Gulf, Trump said they “haven’t thought of it.”

-ABC News' Emily Chang

President Donald Trump said he "might" stay in Europe for the signing of the memorandum of understanding with Iran on Friday, but he wasn’t sure whether that document is the "one I should be signing," suggesting the finalized deal might be what he should appear publicly for.

"This is a memorandum of understanding, it's very important, but it might not be the kind of a document that I should be signing," Trump said during a press conference at the G7.

"We're going to most likely sign a deal. They want to sign a deal. And they've been acting very appropriately,” Trump said.

The president left the door open to future bombing on Iran if the regime didn’t properly adhere to the agreement.

"If it doesn't get done in 60 days, it's all right. We go back to bombing. I don't want to do that because it's so good. But, we might have to because we're never going to let them have a nuclear weapon, but they've agreed not to. And you'll see that very clearly in the agreement,” Trump said.