Negotiations to reopen the Strait of Hormuz are making progress, American and Qatari officials said Tuesday, but a deal with Iran has yet to be announced that could pave the way to reviving a broader cease-fire with the United States.

Secretary of State Marco Rubio said there had been “progress in talks, but not finality yet.” Iran blockaded the Strait of Hormuz — a critical conduit for global oil and gas shipping — after the U.S.-Israeli assault began in late February, causing widespread economic shock.

Iran and neighboring Oman, which also abuts the Persian Gulf waterway, were holding the talks with U.S. input, Mr. Rubio said. The two countries were discussing an immediate solution to the crisis in the strait ahead of a longer-term goal of curbing Iran’s nuclear program, he said.

In Qatar, which has previously acted as a mediator between Iran and the United States, officials expressed a similar measure of optimism. Majed al-Ansari, the Qatari foreign ministry spokesman, told reporters that the negotiations on the strait were in “very progressive stages” as draft language of a possible agreement had been “circulated among the parties.”

Iran’s blockade over the Strait of Hormuz throttled global energy markets and raised pressure on President Trump to end the war. Now, Iran hopes to cement its control over the critical waterway, which has served as a major source of leverage in its dealings with the United States.

U.S. Treasury Secretary Scott Bessent said in a televised interview on Tuesday that he believed an agreement could be imminent. “We are in talks with the Iranians, and I think there is a chance we may have a deal today or tomorrow,” Mr. Bessent said on CNBC.

The price of Brent crude, the global oil benchmark, fell more than 2 percent to about $82 a barrel on Tuesday, as markets appeared to respond to optimism about a potential deal. But repeated pledges of diplomatic progress between the United States and Iran have failed to materialize, with the war now in its sixth month.

The Trump administration had hoped that the short-lived cease-fire, agreed on in June, would reopen the Strait of Hormuz. Instead, it collapsed into renewed fighting, as Iran has sought to impose its authority there.

Iran has enforced its claim by attacking commercial ships as they have tried to transit the strait. That has prompted American bombing runs inside Iran, as well as a U.S. blockade of Iranian ports — neither of which has successfully forced Iran’s leadership to back down.

On Monday, a cargo ship, the Greek-owned Minoan Pioneer, was hit near Oman and one of its crew members was missing, according to the International Maritime Organization. It was unclear who struck the vessel.

Mediators hope that restoring the flow of ships through the Strait of Hormuz will end the current cycle of attacks and counterattacks between the United States and Iran and allow the two countries to return to the June cease-fire agreement. That was supposed to pave the way for talks on the Iranian nuclear program and sanctions relief for Iran’s battered economy.

Over the weekend, Mr. Trump threatened an immense military escalation against Iran before abruptly pulling back, citing pleas for calm from regional allies.

“Our focus right now is on avoiding escalation, reopening the strait and reopening the door for diplomacy between the parties,” said Mr. al-Ansari, the Qatari official. “What we do not want to see right now is a major escalation in our region.”

An arrangement with Iran to reopen the strait could come with a geopolitical cost for the United States. Iranian officials say they are designing the accord to affirm their capacity to control the strait and retain strategic leverage they did not exercise before the war.

Officials familiar with the emerging proposal have said that under the new framework, vessels entering the Persian Gulf would have to transit a channel controlled by Iran, while outbound ships would travel through a channel near Oman.

In recent weeks, the fighting has spread to another vital maritime corridor in the Middle East: the Red Sea. The Houthis, an Iran-backed group that rules much of northwestern Yemen, have vowed to enforce a naval blockade on U.S.-allied Saudi Arabia.

Clashes between the two sides rapidly escalated last month for the first time in years, as Saudi-backed forces bombarded Houthi sites and the Houthis said they had fired at oil and gas facilities in Saudi Arabia.

On Tuesday, the Indian government said a projectile had sunk an Indian-flagged commercial vessel off the Yemeni coast. All 13 Indian nationals on board were rescued, the Indian foreign ministry said. The Houthis did not immediately comment.

Reporting was contributed by Peter Eavis, David E. Sanger, Farnaz Fassihi and Eric Schmitt.