Update: In a social media post late Saturday afternoon, President Trump said that a peace deal with Iran had been "largely negotiated," but noted that "Final aspects and details of the Deal" were "currently being discussed and will be announced shortly." Get the latest coverage here, and read our earlier reporting below.

President Trump told CBS News that negotiators for United States and Iran are "getting a lot closer" to finalizing an agreement between the two countries. 

Sources familiar with the negotiations told CBS News that the latest proposal includes a process to reopen the Strait of Hormuz, the unfreezing of some Iranian assets held in foreign banks, and a continuation of negotiations. 

Mr. Trump declined to provide specifics about the agreement, but said that "every day it gets better and better." 

"I can't tell you before I tell them, right?" Mr. Trump told CBS News in a phone interview. 

Mr. Trump did say that he believes the final agreement will prevent Iran from obtaining a nuclear weapon, adding that he "wouldn't even be talking about it" otherwise. Mr. Trump added that the agreement would also result in Iran's enriched uranium being "satisfactorily handled." 

"I will only sign a deal where we get everything we want," he said. 

Sources told CBS News that Mr. Trump is still mulling proposals and has not made up his mind yet. The sources said he is consulting with advisers and talking to foreign leaders.

Mr. Trump spoke by phone with leaders of Gulf countries and other nations on Saturday afternoon, U.S. officials familiar with the situation said. Counties invited to join the conference call with Mr. Trump to discuss Iran negotiations include Saudi Arabia, Turkey, Egypt, Pakistan, the United Arab Emirates, Jordan, and Qatar, according to sources. One regional official told CBS News that some of the leaders don't know what option Mr. Trump is leaning toward.

Mr. Trump said that if the U.S. and Iran do not come to an agreement, "we're going to have a situation where no country will ever be hit as hard as they're about to be hit." 

Mr. Trump has previously threatened Iran, saying before the start of a ceasefire that began in April that "a whole civilization will die" without a deal, and recently warning the country that "the Clock is Ticking."

Secretary of State Marco Rubio also said Saturday that there "may be news later today" about where negotiations between Iran and the U.S. stand. 

"There's been some progress done, some progress made, even as I speak to you now, there's some work being done," Rubio said, ahead of a formal dinner at the U.S. Embassy in New Delhi, India. "There is a chance that, whether it's later today, tomorrow, in a couple days, we may have something to say, but this issue needs to be solved, as the president said, one way or another."