Iran announced last week that it had enriched uranium past the 3.67 per cent limit set by the nuclear deal, and it has also surpassed the 300-kilogram cap on enriched uranium reserves.
Oil tankers have previously been targeted as the Persian Gulf region took center stage in a crisis over Iran's unravelling nuclear deal with world powers.
Iran, for long, has maintained its ballistic missile program, under the control of its Revolutionary Guard, is for defensive purposes only.
"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.
The European Union is desperately trying to prevent the deal unravelling completely, seeing it as the best way to stop Tehran acquiring atomic weapons.
Hassan Rouhani's official website on Sunday quoted him as saying, "The moment you stop sanctions and bullying, we are ready to negotiate."
The comments by Foreign Secretary Jeremy Hunt late Saturday could help de-escalate tensions that have spiked in recent days.
According to the Mail newspaper on Sunday, the memo was written after the then Foreign Secretary Boris Johnson appealed to the US in 2018 to stick with the nuclear deal, the BBC reported.
Trump and Netanyahu spoke on the telephone on Wednesday, with the US president warning on Twitter of forthcoming "substantially" increased sanctions against Tehran.
The European parties to the deal along with the EU's diplomatic chief on Tuesday called on Tehran to reverse breaches of the agreement.
Iran is still open to negotiations with its European partners and expressed the hope they would 'take steps' toward implementing their commitments.
Iran made the threat to breach the pact by starting uranium enrichment above the agreed limit unless a solution with the global signatories can be found in the next two months.
US Secretary of State, Mike Pompeo said that as long as Iran continues to reject diplomacy and expand its nuclear programme, the economic pressure and diplomatic isolation will intensify.
The deal limited Iran to 300 kilograms of uranium enriched up to 3.67 per cent.
Tehran and Washington have been locked in an escalating standoff since US President Donald Trump unilaterally withdrew from a multi-party 2015 nuclear deal with Iran and reimposed sanctions.