By Kylie Atwood, Alayna Treene and Jennifer Hansler, CNN

(CNN) — President Donald Trump believes his administration is “very close to a solution” on an Iran nuclear agreement and he has personally warned Israeli Prime Minister Benjamin Netanyahu not to disrupt the talks, he said on Wednesday.

Trump cautioned his close ally last week that any move to upend the negotiations would be “inappropriate,” he told reporters.

Sources familiar with the discussions echoed Trump’s optimism and told CNN that they are closing in on a broad agreement that could be clinched when the US and Iran meet next, most likely in the Middle East.

But concerns about Israel derailing the process are clearly high. Asked about reports that he warned Netanyahu against disrupting the talks during a phone call last week, Trump said, “Well, I’d like to be honest. Yes I did.” He added: “It’s not a warning – I said I don’t think it’s appropriate.”

Trump said that his team is having “very good discussions” with Iran. Talks have taken place over the last several weeks led by special envoy to the Middle East Steve Witkoff and moderated by Oman.

“Right now, I think they want to make a deal. And if we can make a deal, I’d save a lot of lives,” Trump said.

Trump’s candid admission about the Netanyahu call follows CNN reporting last week that the US obtained new intelligence suggesting Israel is making preparations to strike Iranian nuclear facilities. Netanyahu has long been a staunch opponent of any kind of deal with Tehran and he applauded Trump’s decision in his first term for the US to exit the nuclear agreement agreed to by President Barack Obama in 2015.

The stakes are enormously high – an Israeli strike could undo the progress the US has made, risk triggering a wider regional conflict and ruin Trump’s chances of achieving a major foreign policy breakthrough as progress on brokering ceasefires in the wars in Ukraine and Gaza has stalled.

Trump’s comments come after Iran’s foreign ministry spokesperson expressed openness to compromises, telling CNN on Monday that there are “so many ways” an agreement on the future of its nuclear program could be reached.

Enrichment has a key focus of talks

Still, the issue of whether Iran would be allowed to enrich uranium remains the key sticking point. And Trump himself acknowledged Iran “still (has) to agree to the final stages of a document.”

The fifth round of talks, which took place in Rome on Friday, dealt more heavily with the question of enrichment.

“Everyone is feeling good,” a Trump administration official said following the talks in Rome. “We have a much better understanding of everyone’s positions.”

The Trump administration had demanded Iran stop all uranium enrichment, which Witkoff has said “enables weaponization” and called a red line in the talks. Uranium, a key nuclear fuel, can be used to build a nuclear bomb if enriched to high levels. Iran has advanced its nuclear program in recent years but also maintains that its program is peaceful. Iran says it is willing to commit not to enrich uranium to weapons-grade as part of an agreement but has said it would reject an outright ban on all enrichment.

Trump – who said that he wants a “very strong document” – seemed to indicate on Wednesday that the current talks have included discussions on increased inspections inside Iran and the dismantling of at least a part of Iran’s nuclear program.

“I want it very strong where we can go in with inspectors. We can take whatever we want, we can blow up whatever we want, but nobody getting killed. We can blow up a lab, but nobody’s going to be in the lab, as opposed to everybody being in the lab and blowing it up,” Trump said.

Trump administration officials, including Witkoff, have said publicly said that the US red line is any Iranian enrichment. But Trump’s comments on Wednesday indicated that he may be open to allowing limited enrichment with inspectors as a solution to the impasse.

Previously, US officials have also floated the idea of Iran importing enriched uranium, rather than doing so in the country – a notion that Iran has repeatedly rejected.

US could invest in Iran’s nuclear power program

The current discussion includes the US possibly investing in Iran’s nuclear power program and standing up a consortium – expected to include nations from the Middle East and the UN’s nuclear watchdog, the International Atomic Energy Agency – that would produce enriched uranium for Iran’s reactors, explained one of the sources.

But nothing has been agreed to regarding Iran’s civilian nuclear energy program, a White House official said.

Iran’s ballistic missile program is not a part of the current discussion, despite some administration officials initially pressing for it to be included. Given how far the talks have advanced at this point sources did not expect an expansion of the topics under discussion. Witkoff in early May suggested that topics other than the nuclear file were “secondary” issues.

“We don’t want to confuse the nuclear discussion because that to us is the existential issue,” he told Breitbart at the time.

Following the Rome talks, the two sides brought the latest proposals to their countries’ respective leaders to confer and are planning to meet again soon, most likely in the Middle East.

The goal is to strike an overall deal at the next meeting between the two sides that lays out specific markers for implementation but also leads to follow-up discussions on technical details, White House officials and sources familiar with the ongoing discussions said.

Witkoff and Michael Anton, the director of policy planning at the State Department, have been taking the lead on all talks in addition to a technical team that has begun working out more specific details for an agreement. However, it is widely expected the technical team will take over and be far more involved once a broad agreement is struck.

Despite Trump touting the expectation of “good news” in the near future, progress in the negotiations has been bumpy at times.

In the fourth round of talks, the US shared a proposal with Iran outlining some of the key requirements the Trump administration is looking for in a deal. But at one point an idea under discussion, which the negotiators on both sides appeared to support, was rejected by Trump, said a source familiar with the matter.

And while Trump is projecting confidence that a deal is on the horizon, he also claimed on Wednesday that the situation “could change at any moment – could change with a phone call.”

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