The United States has made significant progress in negotiations with Iran to reopen the Strait of Hormuz and push forward talks on Tehran’s nuclear programme, but President Donald Trump remains cautious and unwilling to accept a “bad deal”, Secretary of State Marco Rubio said on Monday.

Rubio, currently on a four-day visit to India, said Washington was giving diplomacy “every chance to succeed” even as the two sides continued to negotiate key sticking points, including Iran’s enriched uranium stockpile, sanctions relief and the release of frozen Iranian funds.

“Work is still in progress. We thought we might have some news last night, maybe today,” Rubio told a small group of reporters before leaving for Agra.

“So we have what I think is a pretty solid thing on the table in terms of get the Strait open, enter into a very real, significant time-limited negotiation on the nuclear matters and hopefully we can pull it off,” he said.

Strait of Hormuz, uranium stockpile key sticking points

The Strait of Hormuz — a vital route for nearly one-fifth of global oil and liquefied natural gas shipments before the conflict — has remained severely disrupted since February 28, when joint US-Israeli strikes on Iran triggered retaliatory attacks.

A fragile ceasefire has been in place since April 8, but shipping disruptions have continued.

According to senior Trump administration officials quoted by Reuters, Iran has agreed “in principle” to reopen the Strait of Hormuz in exchange for the lifting of the US naval blockade and has also broadly agreed to dispose of its highly enriched uranium stockpile.

The officials said Iran’s Supreme Leader Ayatollah Mojtaba Khamenei had endorsed the broad framework of the proposed deal, though there was no immediate confirmation from Tehran.

Iranian sources told Reuters that future negotiations could involve “feasible formulas” to dilute the enriched uranium under the supervision of the UN nuclear watchdog.

Trump said on Sunday that the US blockade on Iranian ships in the Strait of Hormuz would “remain in full force and effect until an agreement is reached, certified, and signed”.

“Both sides must take their time and get it right,” he wrote on Truth Social.

Rubio echoed Trump’s cautious tone.

“Every country that we've walked through understands it's not just very reasonable, but it's the right thing for the world to get done. As the President said, he's not in a hurry; he's not going to make a bad deal,” Rubio said.

“The President is not going to make a bad deal. No one has been more serious about the threat of a nuclear Iran than President Trump has been.”

“And so I'm very confident that we should all be very confident that we're either going to have a good agreement or we're going to have to deal with it another way,” he said.

“We'd prefer to have a good agreement.”

Oil prices fall as hopes of breakthrough grow

Optimism surrounding the negotiations pushed oil prices down nearly 6 per cent on Monday to two-week lows, amid hopes that a breakthrough could ease tensions in West Asia and stabilise global energy supplies.

Trump had earlier raised expectations of a possible agreement, saying Washington and Tehran had “largely negotiated” a memorandum of understanding on reopening the Strait and advancing a broader peace process.

However, major disagreements remain over Iran’s nuclear ambitions, sanctions relief, the release of billions of dollars in frozen Iranian oil revenues and regional conflicts involving Iran-backed groups.

Iran has repeatedly denied accusations by the US and Israel that it is pursuing nuclear weapons, insisting its uranium enrichment programme is for civilian purposes.

Rubio comments on Hezbollah, Lebanon situation

Rubio also addressed the situation in Lebanon and tensions involving Hezbollah.

“We're working on it separately. With Lebanon, we are engaged as we have a 45-day ceasefire. We've had weekly meetings now and ongoing daily engagements between the government of Lebanon and Israel,” he said.

Rubio said the “problem” was Hezbollah, not Lebanon.

“Just last night, Hezbollah put out a statement calling for the overthrow of the Lebanese government. And it just reminds you of who you are dealing with here. It (Hezbollah) is a 100 per cent Iranian proxy.”

“As long as an armed Hezbollah exists, it's going to be hard to achieve peace in Lebanon because they're victimising the people of Lebanon,” Rubio said.

“We're going to continue to work on that. Well, Israel always has the right to protect itself. Every country in the world does. And so if Hezbollah is going to launch missiles or launch missiles at them, Israel has every right to respond to that or to prevent that from happening,” he added.

Rubio to visit Taj Mahal, attend Quad meeting

Rubio, who held wide-ranging talks with External Affairs Minister S. Jaishankar in New Delhi, said he was also looking forward to visiting the Taj Mahal during his India trip.

“It's one of the wonders of the world. I think it's important to show respect to the culture of the countries that you visit,” he said.

Rubio will also travel to Jaipur before returning to New Delhi on Tuesday for the Quad foreign ministers’ meeting.

“We have a gap in our schedule because the Quad meeting couldn't happen until tomorrow. So it was a good opportunity to see some of the cultural sites here and pay respect to this country,” he said.

“There's so much to see here, and such a big country with a lot of diversity and a tremendous history. So it'll be a good opportunity to see something that is iconic for the country,” Rubio added.