GEOFF BENNETT: Welcome to the "News Hour."

International mediators tonight are pushing for new peace talks between the U.S.

and Iran, and they're seeking to extend the cease-fire that's set to expire next week.

AMNA NAWAZ: But nothing is set in stone, and the sides remain far apart on issues like the fate of Iran's nuclear program and the Strait of Hormuz.

White House correspondent Liz Landers has been tracking it all and starts our coverage.

LIZ LANDERS: The waters remain quiet through the Strait of Hormuz.

The U.S.

military says its naval blockade of Iran's ports is -- quote -- "fully implemented" as it approaches its third full day.

But with the cease-fire between the U.S.

and Iran expiring in less than a week, beneath the surface and behind the scenes, there's been a flurry of diplomatic conversations.

Regional leaders like Turkey's President Recep Tayyip Erdogan said efforts were under way to restart talks between the U.S.

and Iran and to buy more time.

RECEP TAYYIP ERDOGAN, Turkish President (through translator): We are making the necessary suggestions and attempts to reduce tensions, extend the cease-fire and continue the negotiations.

LIZ LANDERS: More regional officials say they're making progress on both fronts after last weekend's failed talks, including that the U.S.

and Iran have agreed in principle on extending the cease-fire.

Publicly, however, U.S.

and Iranian officials say they have not formally agreed to anything and that engagement continues.

White House Press Secretary Karoline Leavitt today: KAROLINE LEAVITT, White House Press Secretary: That these conversations are productive and ongoing, and that's where we are right now.

I have also seen some reporting about the potentiality for in-person discussions again.

Those discussions are being had, but nothing is official until you hear it from us here at the White House.

LIZ LANDERS: In Iran today, Pakistani military leaders arrived as mediators to discuss plans for a new round of talks.

And Pakistani Prime Minister Shehbaz Sharif, who hosted the last round of talks and is considered a top intermediary, visits Saudi Arabia, Qatar and Turkey through Saturday.

President Trump has suggested that talks could be imminent, and in an interview this morning on FOX Business, he said once again that so could be the end of the war itself.

MARIA BARTIROMO, FOX News Anchor: Well, you keep saying was.

Is this war over?

DONALD TRUMP, President of the United States: I think it's close to over, yes.

I mean, I view it as very close to over.

LIZ LANDERS: But on the biggest sticking point in the talks, any nuclear threat coming from Iran, the president implied a more open-ended mission and again threatened Iran's civilian infrastructure.

DONALD TRUMP: If they're going to have a new nuclear weapon, we will be living with them for a little while, but I don't know how much longer they can survive.

As an example, we could take out every one of their bridges in one hour.

We could take out every one of their power plants, electric power plants, in one hour.

We don't want to do that.

LIZ LANDERS: But many experts say Iran was nowhere near a nuclear weapon.

While visiting Asia today, Rafael Grossi, the head of the United Nations nuclear watchdog, said Iran's nuclear activities are a reality that must be monitored.

RAFAEL GROSSI, Director General, International Atomic Energy Agency: Iran has a very ambitious, wide nuclear program.

So all of that will require the presence of IAEA inspectors.

Otherwise, you will not have an agreement.

You will have an illusion of an agreement.

LIZ LANDERS: At an event with young conservatives last night, Vice President J.D.

Vance said that the U.S.

wouldn't settle for a small deal with Iran.

J.D.

VANCE, Vice President of the United States: Right now, the cease-fire is holding.

And what you're seeing is what the president wants to make, he doesn't want to make like a small deal.

He wants to make the grand bargain.

LIZ LANDERS: But Vance was also heckled in the same event by members of the audience who clearly oppose the wars in the Middle East.

J.D.

VANCE: I certainly think the answer is yes.

And I agree.

Jesus Christ does not -- I agree.

Jesus Christ certainly does not support genocide, whoever yelled that out from the dark.

He certainly does not.

LIZ LANDERS: Vance would acknowledge their concerns.

J.D.

VANCE: I recognize that a lot of young voters don't love the policy that we have in the Middle East, OK?

I understand that.

LIZ LANDERS: Today, in a test of Congress' appetite for prolonging the Iran conflict: MAN: The motion is not agreed to.

LIZ LANDERS: Senate Republicans stood behind President Trump and struck down another Democratic-driven war powers effort to block his ability to launch further strikes.

The treasury secretary today suggested the U.S.

could strike Iran in a different way, economically.

The SCOTT BESSENT, U.S.

Treasury Secretary: Iranians should know that this is going to be the financial equivalent of what we saw in the kinetic activities.

LIZ LANDERS: Regardless of political leanings, almost all Americans are feeling the pain at the gas pump as the result of the war.

Average prices remain above $4 a gallon.

The treasury secretary telling Americans this Tax Day: SCOTT BESSENT: The message is the short-term volatility for long-term gain.

LIZ LANDERS: That optimism will be roundly challenged in the waters of the Gulf, as the White House navigates a tense and narrow strait.

For the "PBS News Hour," I'm Liz Landers.