Tehran said US President Donald Trump and Vice President Mike Pence in "numerous absurd tweets, (had) incited Iranians to engage in disruptive acts" which violated international law, CNN reported.
Twenty-one people died in six days of protests sparked by Iran's economic problems, which spanned several cities.
On Thursday, the state media focused on pro-government rallies after a second night without reports of major protests.
The unrest was initially over price rises and corruption but the focus quickly turned to the remote elite and particularly Supreme Leader Ayatollah Ali Khamenei.
The protests are the largest since the disputed 2009 presidential election. Millions took to the streets that time against the election of President Mahmoud Ahmadinejad.
Since the protests broke out, Trump has endorsed them, culminating on Wednesday with the suggestion that the US could offer "great support" to protesters.
In his letter, Iranian UN envoy Gholamali Khoshroo said the US had a track record of intervening in Iranian affairs.
However, he added, the current administration had "crossed every limit in flouting rules and principles of international law governing the civilized conduct of international relations".
The letter also pointed to a US State Department official's statement earlier this week that Washington was communicating with anti-government protesters in Iran through its Facebook and Twitter pages in Farsi, and was encouraging them to rally.
The Iranian UN envoy said that the US had actually insulted Iranians by banning them from entering the country (under Trump's travel ban) and with the US President's refusal to certify an internationally agreed deal to limit Tehran's nuclear programme.
The Russian Foreign Ministry echoed the concerns, urging the US not to interfere in Iran's "domestic issues", Russia's Itar-Tass news agency reported.
The anti-government protests, the most powerful challenge to the regime in years, appeared to have fizzled, following a claim by Revolutionary Guards commander Mohammad Ali Jafari that the unrest was officially over.
The Iranian government had restricted the use of social-media apps Telegram and Instagram to quell the unrest. It has said those restrictions will be lifted on Friday, and there were signs that it had begun easing some of them.
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
