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President Biden wants to return to the 2015 deal after former President Donald Trump withdrew in 2018. The U.S. decision to quit the deal and impose sweeping sanctions on Iran prompted Tehran to breach many of the key restrictions in the accord, making a return to the agreement’s provisions and limits difficult for both sides.

Senior officials in Vienna this week wrapped up five days of talks, with delegations returning home before negotiations resume next week. People involved in the talks say progress has come as the U.S. laid out more clearly the contours of the sanctions relief it is prepared to provide.

Many of the sanctions were imposed under Mr. Trump using U.S. terrorism authorities, and U.S. officials previously have said they are willing to consider lifting some of them. But they haven’t detailed which sanctions could be eased or which Iranian entities stand to be affected.

Two people familiar with the matter said the U.S. is open to lifting terror sanctions against Iran’s central bank, its national oil and tanker companies and several key economic sectors including steel, aluminum and others. A senior European official said Washington has also signaled potential sanctions relief for sectors including textiles, autos, shipping and insurance, all industries Iran was earmarked to gain from in the 2015 agreement.

Lifting terror sanctions against some of those state entities and critical sectors of the economy would act as a significant tonic to the crippled economy and represent a large share of the country’s income.

U.S. officials in Vienna outlined the types of sanctions relief that were being considered, though without offering a detailed proposal, according to the people familiar with the matter.

The two sides are at odds over Iran’s request that the U.S. lift its sweeping “foreign terrorist organization” designation of Iran’s elite military force, the Islamic Revolutionary Guard Corps. The U.S. isn’t currently considering lifting terror sanctions on the IRGC, the people familiar with the matter said.

Also likely to prove contentious is the U.S. terror listing of the office of Iran’s Supreme Leader Ali Khamenei, officials said.

While the Biden administration has said it was prepared to roll back sanctions levied by Mr. Trump, officials also have said they reserve the right to retain some of the actions against Tehran’s support for militant groups and its ballistic missile program.

On Wednesday, Iranian President Hassan Rouhani said U.S. officials seemed serious in their offer to lift sanctions. But he said Washington must go beyond generalities and spell out exact details.

“In some steps, we found them serious,” he said. “In some steps they speak equivocally. Now we should see.”

A senior State Department official said Wednesday that the U.S. provided Iran with examples of sanctions Washington would negotiate to secure a deal.

“I think they have a pretty clear sense at this point about our view about the sanctions that we’re going to have to lift,” and those “that we would not lift,” the official said.

Iran reduced its compliance with the 2015 agreement following the Trump administration’s withdrawal, expanding its uranium enrichment operations. An Iranian official said a return to the nuclear agreement would only end 800 new U.S. sanctions and terror designations, just about half the 1,500 that Iran estimates have been imposed on its economic sectors, institutions, companies and individuals.

Disentangling Iran’s complex web of sanctions is a politically sticky task for the Biden team. Opposition to a potential agreement is building among Republican critics of the Biden administration. A group of Republican senators is pushing legislation giving Congress the power to prevent the administration from lifting any of the Iran sanctions.

Proponents of keeping the sanctions in force say that any relief would undermine leverage that Washington has for securing a new, strengthened deal, pointing to Tehran’s available currency reserves falling to their lowest point in decades. That figure is offset by a surge in Iranian oil exports since the Biden administration has taken office, with China taking much of the new output amid perceptions of Washington taking a more lenient approach to Iran.

There also has been progress in talks on Iran’s path toward compliance with the 2015 agreement, which have narrowed to what to do with its three-ton stockpile of enriched uranium, and what happens to the advanced machines Tehran has installed to generate nuclear fuel more quickly.

Officials also said Iran had moved away in the talks from insisting that the U.S. reverse all sanctions imposed since 2015, when the nuclear deal was implemented. Iran’s chief nuclear negotiator, Abbas Araghchi, told The Wall Street Journal last week that although Tehran’s demand was an end to all sanctions, it was willing to negotiate that demand.

Hard-liners in Tehran, however, have disagreed in public with Mr. Araghchi, setting up domestic tension that worries Western officials. The state-run English-language Press TV on Tuesday quoted an informed source as saying that Iran didn’t accept a sequential lifting of sanctions, and that Iran would have to verify any sanctions relief before reciprocating, which would take up to six months.

The parties to the 2015 deal, which also include France, Germany, Russia, China and Britain, have agreed to set up a new group to tackle a central challenge in the talks—matching up precisely what steps the U.S. and Iran must take, and when, on sanctions lifting and reversing Iran’s breaches of the deal.

Negotiators also said this week they began drafting texts of potential agreements that can be discussed in coming sessions.

Mikhail Ulyanov, Russia’s ambassador to the United Nations atomic agency and chief negotiator at the talks, told the Journal that work had begun on drafting steps the two sides would have to take to restore the agreement. He said negotiations could be complete by late May, when an agreement ensuring continued International Atomic Energy Agency oversight of Iran’s nuclear activities expires.

“I do not believe there are insurmountable obstacles to a deal,” he said.