Secretary Marco Rubio suggested to Fox News in an interview on Monday that Iran's peace proposal falls short of the U.S. conditions for ending the war, now entering its third month.

Two officials familiar with the matter told ABC News that the Iranian proposal consists of a loosening of Tehran's grip on the Strait of Hormuz in exchange for the lifting of the U.S. blockade. Talks on Iran's nuclear program would then be pushed back to an unspecified future date, Tehran's proposal suggested.

Rubio, though, said the nuclear issue was at the heart of the U.S. position. "The nuclear question is the reason why we're in this in the first place," Rubio said.

Rubio also said the U.S. would not allow Tehran to retain control over the Strait of Hormuz, or to continue to charge tolls to shipping passing through.

"Those are international waterways. They cannot normalize, nor can we tolerate them trying to normalize, a system in which the Iranians decide who gets to use an international waterway and how much you have to pay them to use it," he said.

Rubio underscored U.S. concerns about the regime's ability to agree to a deal and the status of new Supreme Leader Mojtaba Khamenei.

"One of the impediments here is that our negotiators aren't just negotiating with Iranians. Those Iranians then have to negotiate with other Iranians in order to figure out what they can agree to, what they can offer, what they're willing to do, even who they're willing to meet with," Rubio said.

Asked whether he believed Mojtaba Khamenei was still alive, Rubio replied, "We have indications that he is. Obviously they claim that he is. We don't have evidence that he's not."

"I think the question between alive and in power are two different questions. You can be alive -- but I think the unresolved questions here are does he have the same credibility as his father did," Rubio said.

Rubio also suggested that the Iranian proposal may not have the backing of all factions jostling for influence in Tehran. "I think there are still questions about whether the person submitting it had the authority to submit that offer," he said.

Nonetheless, Rubio said he believed the Iranians "are serious about getting themselves out of the mess that they're in."

-ABC News' Shannon K. Kingston

The Israeli military said Monday it was striking Hezbollah infrastructure in southern Lebanon and further northeast in the Beqaa Valley area.

The Israeli military also accused Hezbollah of violating the ceasefire, saying Hezbollah launched several drones at IDF forces in southern Lebanon.

Hezbollah issued two statements referring to these attacks as responses to Israel's own violations of the ceasefire. Hezbollah said the drones targeted an Israeli tank and an Israeli bulldozer "while it was demolishing homes in the city of Bint Jbeil," which it said was "in response to the Israeli enemy’s violation of the ceasefire and the demolition of homes in villages of southern Lebanon."

-ABC News’ Victoria Beaulé

In an address to students on Monday, German Chancellor Friedrich Merz said the U.S. has “no strategy” with Iran.

“I cannot see what strategic exit the Americans are now opting for, especially as the Iranians are obviously negotiating very skillfully -- or, rather, very skillfully not negotiating and letting the Americans travel to Islamabad [in Pakistan] only to leave again without any results,” Merz said. “An entire nation is being humiliated by the Iranian state leadership, particularly through these so-called Revolutionary Guards."

"We offered, as Europeans -- and said that we were willing -- after the end of negotiations to help getting the Strait of Hormuz open again,” he continued. “... We can help there but first the fighting needs to end. And at the moment I do not see how this can be realized in the near future because the Iranians are clearly stronger than one thought and the Americans clearly don't seem to have a convincing negotiating strategy.”

-ABC News’ Victoria Beaulé

Kremlin spokesperson Dmitry Peskov told reporters that Iranian Foreign Minister Abbas Araghchi is due to meet with Russian President Vladimir Putin on Monday, as part of the Iranian diplomat's visit to St. Petersburg.

"The significance of this conversation is hard to overestimate in terms of how the situation around Iran and in the Middle East is developing," Peskov said.

Putin will meet with Araghchi at St. Petersburg's Presidential Library, Peskov said.

-ABC News' Joe Simonetti

Moments after announcing an extended ceasefire between Israel and Lebanon, President Donald Trump said "we hope" there's three weeks of "no firing" between the two countries.

"But they do have Hezbollah to think about, and we're going to be working with Lebanon to get things straightened out in that country," he said during surprise remarks from the Oval Office while flanked by Secretary of State Marco Rubio and Vice President JD Vance.

Trump also said he expects the president of Lebanon and the prime minister of Israel to come to the White House "over the next couple of weeks" while the ceasefire is in place, though he did not provide any specifics of such potential travel.

Trump expressed his hope that the Israel-Lebanon conflict will get "worked out simultaneously with what we're doing in Iran."

-ABC News' Michelle Stoddart, Isabella Murray and Emily Chang