"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, told the media at a briefing on Monday.
"The Secretariat is in close contact with the permanent missions of the US and Iran to the UN regarding this matter and has conveyed its concerns to the host country."
On Sunday, US Secretary of State Mike Pompeo said that he has granted a visa for Zarif to visit the UN headquarters in New York, adding that the latter's movements will be largely confined, Xinhua news agency reported.
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," he added.
The Iranian Foreign Minister is in New York to attend a meeting of the UN Economic and Social Council, a high-level ministerial meeting on sustainable development goals for issues that include conflict, hunger, gender equality and climate change, according to The Washington Post.
His visa was issued at the US Embassy in Bern, Switzerland on Sunday, a day before he arrived in New York.
The US has an agreement that requires it to issue visas expeditiously to all foreign diplomats travelling to New York for UN events.
( With inputs from IANS )