Trump says US Navy attacked and seized Iranian-flagged cargo ship

Secretary of State Marco Rubio will now participate in the talks between Israeli and Lebanese ambassadors in D.C. on Tuesday, according to a State Department official.

"This conversation will scope the ongoing dialogue about how to ensure the long-term security of Israel's northern border and to support the Government of Lebanon's determination to reclaim full sovereignty over its territory and political life," the official said. "Israel is at war with Hizballah, not Lebanon, so there is no reason the two neighbors should not be talking."

-ABC News' Shannon K. Kingston

Vice President JD Vance talked about the weekend negotiations with Iran and what the U.S. red lines are in an interview with Fox News on Monday.

When asked about what went wrong that led to the talks falling apart, Vance noted that there were things that "went right" during the talks.

"We made a lot of progress, but we also made very clear, and I think this is part of the progress we made, what the terms where the United States could make some accommodation, what terms we were flexible on, and what things we absolutely needed to see in order for the president of the United States to feel like he was getting a good deal," Vance said.

Vance said that all of the United States' red lines in the negotiations stemmed from the Iranians never having a nuclear weapon. The two crucial pieces that the U.S. side is not flexible on are, according to Vance, the U.S. getting possession of the "nuclear dust" -- the enriched uranium that Iran currently possesses -- and a "mechanism to ensure" that Iran won't have the ability to enrich uranium.

Vance said the opening of the Strait of Hormuz did come up, and that the "Iranians tried to move the goal post during the negotiation."

"Our expectation is that the Iranians are going to continue to make progress to opening the Straits of Hormuz, and if they don't, it's going to fundamentally change the negotiation that we have with them," Vance said.

-ABC News' Hannah Demissie, Meghan Mistry and Michelle Stoddart

The leader of Hezbollah said in an address Monday that they "reject" the negotiations set to take place between Lebanese and Israeli ambassadors in Washington, D.C., on Tuesday.

"We reject negotiations with the usurping entity," Naim Qassem said. "These negotiations are futile and require Lebanese consensus to change the direction from non-negotiation to direct negotiation."

Qassem also vowed that the militant group won't surrender.

"We will not surrender and will remain in the field until our last breath," he said. "We will confront and demand justice, and we want to set an example for the entire world that Lebanon, with its army, people, and resistance, is unyielding against the enemy."

Mediators have launched into a flurry of activity aimed at getting negotiations between the U.S. and Iran back on track as they hope to arrange another round of talks between the parties before the two-week ceasefire expires, according to two U.S. officials and another source with knowledge of the situation.

Even though the U.S. and Iran have been accusing each other of violating the truce since its implementation, mediators see its looming end as a potentially useful tool for ramping up pressure on both sides to come to the table, according to the officials and source.

The officials and other source say mediators are trying to stave off a resumption of attacks on Iran from the U.S. and push Tehran to reconsider a proposal put forward by the Trump administration during the Islamabad talks.

When asked at the White House Monday about the negotiations with Iran, President Donald Trump said "we've been called by the other side," and that "they'd like to make a deal very badly, very badly.”

Both the U.S. and Iran have expressed interest in continuing to work toward a diplomatic settlement, the officials and source said.

-ABC News' Shannon K. Kingston