The United Nations has told the United States that it is concerned over the restrictive travel measures imposed on Iran's foreign minister, a UN spokesman said on Monday.

"The Secretariat is aware of the restrictive travel measures recently imposed by the host country on personnel of the permanent mission of Iran to the UN," said Farhan Haq, deputy spokesman for UN Secretary-General Antonio Guterres.

"The Secretariat is in close contact with the permanent missions of the United States and Iran to the United Nations regarding this matter and has conveyed its concerns to the host country," Haq told reporters at a regular briefing.

US Secretary of State Mike Pompeo said on Sunday he had greenlighted a visa for Iranian Foreign Minister Mohammad Javad Zarif to visit the United Nations headquarters in New York, adding that Zarif's movements will be largely confined.

Zarif and other members of the Iranian delegation, who arrived in New York on Sunday, will be allowed to travel between the UN headquarters and the Iranian mission, and to the residence of Iran's UN ambassador nearby, Pompeo told The Washington Post.

"US diplomats don't roam around Tehran, so we don't see any reason for Iranian diplomats to roam freely around New York City, either," the Post quoted Pompeo as saying.

Since Washington pulled out of the 2015 Iran nuclear deal last year, relations between the two countries have deteriorated with increasing tension in the Gulf of Oman, Persian Gulf and the Strait of Hormuz and the reinstatement of sanctions against Iran.

Haq said Guterres has made it very clear that the Iran nuclear agreement is a very significant achievement.

"The secretary-general has repeatedly called for all parties to abide by the terms of the agreement and has made clear that we need to keep this preserved. Otherwise, there is the possibility, as he has repeatedly warned, of a confrontation in a region that has had far too many tensions," Haq said.