Israeli Prime Minister Benjamin Netanyahu has not officially responded to President Donald Trump's remarks that a U.S. deal with Iran has been "largely negotiated."

But a statement attributed to an Israeli political source was distributed to the local press with details of the Israeli leader's call with Trump on Saturday that focused on the emerging deal.

"The U.S. is updating Israel on the negotiations for a memorandum of understanding to open the Strait of Hormuz and entering into negotiations for a final agreement on the points that are in dispute," the source said.

"In a conversation last night with President Trump, the prime minister emphasized that Israel will maintain freedom of action against threats in all arenas, including Lebanon, and President Trump reiterated this principle," the source added.

"President Trump made it clear that he will stand firm in the negotiations on his consistent demand for dismantling the Iranian nuclear program and removing all enriched uranium from its territory, and that he will not sign a final agreement without accepting these conditions," the source said.

Netanyahu "reiterated his appreciation to President Trump for his long-standing and extraordinary commitment to Israel's security," the source said.

-ABC News' Jordana Miller and Rashid Haddou-Riff

A source familiar with the situation told ABC News on Sunday that there is "serious concern and disappointment" in Israeli Prime Minister Benjamin Netanyahu's office over a possible deal between the U.S. and Iran to end the ongoing war. The source said that Israeli efforts are ongoing "to improve the outcome of the deal."

An Israeli official told ABC News that the emerging deal appears to be bad because "it signals to the Iranians they have a weapon no less effective than nuclear weapons, and that is the Strait of Hormuz." The official added that it is unclear what will happen after the first phase of the peace deal.

Netanyahu is expected to hold a security meeting with his top defense officials at 7 p.m. local time (12 p.m. ET) to discuss the emerging deal, an Israeli official told ABC News.

-ABC News' Jordana Miller and Rashid Haddou-Riff

Pakistani Prime Minister Shehbaz Sharif congratulated President Donald Trump on his "extraordinary efforts to pursue peace" with Iran in a post posted on X on Sunday, expressing hope to "host the next round of talks very soon."

Trump, Sharif said, had a "productive telephone call earlier today, with the leaders of Saudi Arabia, Qatar, Turkiye, Egypt, the UAE, Jordan and Pakistan." Sharif said Pakistan's army chief -- Field Marshal Syed Asim Munir -- took part in the call.

"Pakistan will continue its peace efforts with utmost sincerity," Sharif wrote.

-ABC News' Rashid Haddou-Riffi and Habibullah Khan

Secretary of State Marco Rubio said on Sunday that the U.S. has made "significant progress" in discussions related to Iran, while stressing the "ultimate goal is that Iran can never have a nuclear weapon."

Speaking during his visit to India in a press conference with Indian External Affairs Minister Subrahmanyam Jaishankar, Rubio said that additional developments could come later on Sunday.

Rubio added that the administration has worked with Gulf regional partners over the last 48 hours on a possible framework aimed at keeping international waterways open and addressing concerns surrounding Iran's nuclear ambitions.

"We think we've made some progress on the outline of something that, if it works, could give us that outcome," Rubio said, while cautioning that any agreement would still require "full Iranian acceptance, and then compliance."

He also condemned Iranian threats against commercial shipping routes, calling such actions "illegal under any concept of international law."

Rubio defended President Donald Trump's record on Iran, stating "there is no one who has been stronger on this issue than President Trump," dismissing suggestions that the administration would agree to any arrangement that strengthens Iran's nuclear capabilities.

"The idea that somehow this president, given everything he's already proven he's willing to do, is going to somehow agree to a deal that ultimately winds up putting Iran in a stronger position when it comes to nuclear ambitions is absurd," Rubio said.

Rubio closed his remarks by expressing cautious optimism, saying "perhaps there is the possibility that over the next few hours the world will get some good news."

-ABC News' Rebecca Gelpi-Ufret

Secretary of State Marco Rubio spoke with reporters following his meeting with India’s Prime Minister Modi earlier Saturday, saying negotiations remain ongoing but that there "may be news" Saturday or in the coming days.

"There may be news later today. I don't have news for you at this very moment, but there might be some news a little later today, there may not be. I hope there will be, but I'm not sure yet," Rubio said.

Rubio stressed that "some progress" has been made with respect to Iran, before emphasizing the U.S. position on Iran not having a nuclear weapon, opening the Strait of Hormuz without a toll, and turning over enriched uranium.

"Even as I speak to you now, there's some work being done. There is a chance that whether it's later today, tomorrow, and a couple days, we may have something to say, but this issue needs to be solved as the president’s said, 'one way or the other'," Rubio said.