Iran live updates: Tehran has 'no plans' for new round of talks, spokesperson says

The Rich Starry, one of the U.S.-sanctioned tankers that approached the Strait of Hormuz on Monday before turning around, appeared on Tuesday to have successfully transited the waterway, according to data from Kpler-owned ship tracking firm Marine Traffic and Michelle Bockmann, a shipping analyst with the maritime AI company Windward.

The tanker crossed from the Persian Gulf into the Gulf of Oman before appearing to stop just beyond the eastern mouth of the Strait. Several other ships are in the same area and transmitting as being at anchor, according to Marine Traffic.

Elpis, the U.S.-sanctioned tanker that made the crossing on Monday, also appeared to have stalled immediately after its exit at the eastern mouth of the Strait, according to Marine Traffic and Eurasia Group analyst Gregory Brew.

Marine Traffic data and Bockmann indicated that the Murlikishan -- a chemical tanker sanctioned by the U.S. in 2020 for its ties with Iran -- crossed the Strait of Hormuz heading west on Tuesday morning.

The Murlikishan crossed from the Gulf of Oman into the Persian Gulf. The vessel appeared to have already been in the Gulf of Oman when the U.S. blockade of Iranian ports in the Strait of Hormuz started on Monday.

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.

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.

President Donald Trump touted U.S. military action against Iran's Navy on Monday, moments after the 10 a.m. ET deadline he set for when he said American troops would start enforcing a blockade of all maritime traffic entering and exiting Iranian ports in the Strait of Hormuz.

"Iran's Navy is laying at the bottom of the sea, completely obliterated - 158 ships," Trump wrote on social media, claiming that he hadn't ordered strikes on "fast attack ships" because they aren't a threat.

On Saturday, CENTCOM confirmed Trump's announcement that the U.S. military had begun mine-clearing operations to ensure safe passage through the Strait.

Trump threatened in his post on Monday, "If any of these ships come anywhere close to our BLOCKADE, they will be immediately ELIMINATED, using the same system of kill that we use against the drug dealers on boats at Sea. It is quick and brutal."