The partial easing of sanctions on Iran in the weekend nuclear deal will only have a small benefit for the Iranian economy, a senior US Treasury official said Monday.

The official said that the country's economy remains in deep recession and will get little boost from the narrow measures agreed to expand Tehran's access to international trade and finance.

"In relation to the depth of the economic distress that Iran is currently facing, this package is really quite modest and economically insignificant," the official said in a briefing for journalists.

"It will not move the needle" in terms of the country's economic performance.

The official, who declined to be named, also warned international businesses that most sanctions remain in place on Iran and said they should not assume they can trade freely with the country now.

"Any business, any bank, any broker, anybody who thinks it's open season to go into Iran today, I think is sorely mistaken. We will enforce these sanctions," the official said.

The United States and its allies reached a deal with Tehran on Saturday to lighten some of the tough sanctions on the country in exchange for it limiting its uranium enrichment operations, which many believe underpins an effort to build nuclear weapons.

The deal delivers about $7 billion in relief to Iran, according to US estimates, and will stand for six months while a more long-lasting solution is negotiated.

The relief includes giving Iran very limited access to its income from oil and other sales, frozen in banks overseas, to be used for humanitarian purposes.

It allows the country to export petrochemicals and trade in gold, to buy medical equipment and parts for civilian aircraft, to help its auto industry and to pay overseas tuition for students.

It also protects the country's oil exports at their current levels, preventing the parties to the deal from trying to force more cutbacks.

That, the Treasury official stressed, was only a modest concession that would not allow Iran's deeply curtailed oil exports to grow.

"The size of this deal is just not economically significant to Iran," the official said.

"The vast bulk of our sanctions that we have built up over time all remain in place. We'll be continuing to apply the pressure on Iranians just as we have in the past."