AMNA NAWAZ: Welcome to the "News Hour."

On this Memorial Day, Iranian and U.S.

officials agree progress to end the war has been made, but how much remains uncertain.

President Trump suggested this weekend that a deal was close, before saying that the U.S.

is in no rush to reach an agreement.

As negotiations resume today in Doha with a visit by senior Iranian officials.

Iran acknowledged an agreement on many points, but said the signing of a deal was not imminent.

Nick Schifrin's been tracking the statements and updates, and he joins us here now.

So, Nick, let's start with the U.S.

The president was very positive over the weekend about the potential for a deal.

NICK SCHIFRIN: He was, yes.

AMNA NAWAZ: What did he say today?

NICK SCHIFRIN: He was very much on the fence about the possibility of a deal today.

This is what he wrote on TRUTH Social this morning: "It will only be a great deal for all or no deal at all, back to the battlefront and shooting but bigger and stronger than ever before, and nobody wants that."

But, as you said, on Saturday, he wrote that an agreement had largely been negotiated.

And that led to prominent public criticism from Israel and some Republican allies that want to restart the war.

So what's in the deal?

A senior administration official brief reporters this weekend.

A European and a regional official confirmed that this is the outline of the deal as it is right now.

In the first phase, Iran would open the Strait of Hormuz and the U.S.

would end its blockade.

Number two, the war would end, including Lebanon.

We will talk, Amna, more about that in a moment.

And the third phase is in principle agreements.

Iran limits its nuclear program and the U.S.

lifts its sanctions.

And if that third point sounds familiar Amna, it is.

That is the core of the 2015 JCPOA nuclear deal and it's also the core of this deal.

So that brings us to the second phase.

Iran would freeze its uranium enrichment for TBD years, likely somewhere between 10 and 20 years, but that is still under the negotiation.

Number two, Iran would export its nearly 1,000 pounds of highly enriched uranium.

The senior administration official admitted there's a question about how precisely to do that, but did say the supreme leader had signed off on that in principle, and an Iranian official has told me that Iran is willing to export to the IAEA, but not to the U.S.

And, thirdly, in exchange for all that, the core of the U.S.

offer, lifting sanctions, unfreezing assets.

A senior administration official said the more accommodations that Iran makes, the more money the U.S.

would free up.

As the official put it -- quote -- "No dust, no dollars," a reference to the enriched uranium.

But the senior administration official acknowledged, Amna, that there is no guarantee, in this person's words, that this makes it through the Iranian system and lots of details to be worked out.

AMNA NAWAZ: Meanwhile, we saw President Trump also try to expand the negotiations?

Tell us about that.

NICK SCHIFRIN: Yes, so the president has spoken multiple times to regional leaders and really beyond the region, some of the people, some of the countries that are helping mediate, and that he is now pressuring them.

And he said that, if Iran and the U.S.

signs this deal, then they must sign a deal with Israel.

This is what he wrote: "I am mandatorily requesting that all countries immediately sign the Abraham Accords."

Now, today, the Abraham Accords includes the UAE, Bahrain, as well as Morocco and Kazakstan in green there.

The president announced today that Saudi Arabia and Qatar would be required to join, followed by Pakistan, Turkey, Egypt and Jordan, and he said, if they don't, they're showing -- quote -- "bad intention."

So, clearly, he's trying to sweeten the deal, but it's left a sour taste in some regional officials' mouths who I have spoken to.

They were very shocked about some of this language, almost the threat that the president made.

And let's be clear, Amna, this is dead on arrival.

The Saudis reiterated today that the only way they will normalize with Israel is that if Israel undergoes a -- quote -- "irreversible path toward Palestinian statehood."

AMNA NAWAZ: You mentioned talking to some Iranian officials.

What are we hearing publicly from Iran today on all of this?

NICK SCHIFRIN: As you said at the top, Iran's top negotiators visited Doha today.

And we have seen in the U.S.

concern about Iran's leadership being fragmented.

Well, Iran's Foreign Ministry spokesperson today did acknowledge some progress, but blamed American leadership for the holdups.

ESMAEIL BAGHAEI, Iranian Foreign Ministry Spokesman (through translator): It is true that we have reached a conclusion regarding a large part of the topics under discussion.

But to say that this means the signing of an agreement is imminent, no one can make such a claim, because policymaking and decision-making in America have become caught in a kind of institutionalized instability.

NICK SCHIFRIN: As for Iran's promises, at this point, Amna, there is no public confirmation that Iran is willing at all to restrict its nuclear program going forward.

AMNA NAWAZ: Meanwhile, this is a war that the U.S.

and Israel launched together in Iran.

What's Israel saying about the possibility of a deal?

NICK SCHIFRIN: Israeli officials publicly questioned the deal, calling it -- quote -- "a bad deal" this weekend.

Today, a senior Israeli official messaged me, saying that the president told Prime Minister Benjamin Netanyahu that the president will remove all of the enriched uranium from Iran, not just highly enriched uranium, all enriched uranium for Iran.

I'm not sure if that's accurate, but Israel is pushing on another subject, and that is Lebanon.

Today, Israel announced that it had hit some 70 sites across the country today, what it called Hezbollah command centers and weapons storage facilities.

Lebanese officials have said that 3,100 people have been killed in Lebanon since March.

Iranian officials do tell, Amna, that part of this deal is Israel stopping in Lebanon, but U.S.

officials today blamed Hezbollah, not Israel, and said that Israel -- quote -- "would never be expected to passively absorb any attacks."

AMNA NAWAZ: We will see what happens next.

Nick Schifrin tracking it all.

Thank you, Nick.

NICK SCHIFRIN: Thank you.