CAIRO (AP) — The United States is close to reaching a deal with Iran that would end the war, reopen the Strait of Hormuz and see Iran give up its stockpile of highly enriched uranium, regional officials told The Associated Press on Sunday, though U.S. President Donald Trump said he told representatives "not to rush into a deal."

Trump said negotiations were "proceeding in an orderly and constructive manner," and the relationship with Iran was becoming "much more professional and productive." He pushed back against criticism by some fellow Republicans seeking a tougher approach.

READ MORE: Trump says deal with Iran, including opening Strait of Hormuz, is 'largely negotiated'

The agreement would not be signed Sunday, according to a person familiar with the status of negotiations who spoke on condition of anonymity because they were not authorized to comment publicly. The sides have previously seemed close to a deal in recent weeks, only to falter.

The strait's reopening would ease a worldwide energy crisis sparked by the U.S. and Israeli bombardment of Iran on Feb. 28, which led Tehran to effectively close the waterway. Prices have spiked for oil, gas and related products. Experts say it would take several weeks or even months for shipping and prices to recover once the strait reopens.