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

The U.S. proposed a 20-year minimum suspension on Iranian uranium enrichment rather than a permanent end to enrichment amid negotiations to end the war with the country, a source familiar with the negotiations told ABC News on Monday.

The source said that in addition to the suspension, the U.S. also suggested "all kinds" of other restrictions but did not immediately elaborate on what they were.

The news comes as The New York Times reported on Monday that the U.S. had asked for a 20-year suspension, with the Iranians formally responding on Monday that they would agree to suspend enrichment for up to five years. The paper reported that the president had rejected that offer.

The White House did not respond to ABC News' request for comment on the Iranian proposal nor the president’s reaction to it.

-ABC News' Nicholas Kerr

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."