AMNA NAWAZ: Welcome to the "News Hour."

The U.S.

and Iran both say they are inching closer to a deal today to end the war that the U.S.

and Israel started with Iran nearly four months ago.

GEOFF BENNETT: But as with previous announcements, from the U.S.

side in particular, there was little in the way of detail on timing and execution of any agreement and major differences in the public pronouncements of what exactly is in this so-called memorandum of understanding.

Our White House correspondent, Liz Landers, has been reporting on this all day and is here to update us.

So, Liz, you were on a briefing call today with a senior White House official.

What is the White House saying is in this deal?

LIZ LANDERS: Yes, this call was held because the administration says that they are tired of seeing misreporting and the back-and-forth that we have seen play out on social media about this.

So a senior U.S.

official laid out what the U.S.

is asking for right now and what these demands are from the U.S.

side.

First of all, they're demanding that the Strait of Hormuz be open and that this would lift the blockade, secondly, dismantling of the Iranian nuclear program and the U.S.

removes that enriched uranium material, that it will be destroyed on site and then taken out of the country.

That this would also guarantee for a long-term peace in the region, that Iran would no longer fund proxy groups that are violent towards other countries, and that Iran's territorial sovereignty would also be respected, and then, finally, enforceable inspection regimen with a long-term commitment.

Now, Geoff, in exchange for all of this, Iran would get sanctions relief, which has been crippling for that country for a number of years now.

This official said that, going forward, they would get rewarded for - - quote -- "acting like a normal country."

This official was optimistic that the U.S.

and Iran could reach this deal, saying they were about 80 to 85 percent of the way there.

They did not give a timeline on when this could be signed, but acknowledged that it could happen in Europe.

GEOFF BENNETT: Eighty to 85 percent of the way there.

What about the sticking points over Iran's nuclear program?

LIZ LANDERS: That remains a sticking point.

And this U.S.

official did acknowledge that, saying that they do believe that this is a direct line to those things, but said -- quote -- "They are committing indefinitely to not build or procure a nuclear weapon.

And then, you know, we're going to have to figure out exactly how we enforce that."

And, Geoff, we have heard a number of times from the president back and forth over the last few months about striking a deal.

We will see if this becomes the sticking point again.

GEOFF BENNETT: And, Liz, today, there have been conflicting messages from Iran about what they think is in the deal.

Bring us up to speed.

LIZ LANDERS: The Iranians posted on social media.

An Iranian media outlet said this morning that there was a 14-point draft memorandum.

They posted about this not.

Long afterwards, we heard from President Trump on his social media platform saying that there was a lot of false information that was floating around out there.

And not long after that, we heard from the Iranian foreign minister saying that the memorandum of understanding has never been closer, and then the president reposted that.

So, seeming like the Americans and Iranians were sort of getting on the same page here.

Now, though, this afternoon, we have heard from Iran's foreign minister, Araghchi, saying that the terms of the nuclear agreement have to come at a later stage after this first cease-fire is agreed to.

He said on Iranian state TV that the cease-fire must include Lebanon in part of this and that Israel must stop striking in that country, as Hezbollah and Israel have been exchanging strikes for weeks now.

Araghchi also said that the management of the Strait of Hormuz would not return to the prewar era, that the sovereignty of the Strait of Hormuz belonged to Iran and Oman, that Iranian frozen funds would be released.

This could also be a sticking point.

And that, most importantly, I think, downblending the highly enriched uranium stockpile.

That is very different than what we heard from the U.S.

official.

GEOFF BENNETT: Lots to track, to say the least.

Liz Landers, thanks, as always.

LIZ LANDERS: Of course.