The pair faced court on on Monday charged with federal terrorism-related crimes, according to court records.
Emir Balat, 18, and Ibrahim Kayumi, 19, are accused of travelling from Pennsylvania with dangerous improvised explosive devices to Manhattan on Saturday, where a small group of far-right Christian activists had planned the anti-Muslim rally outside Gracie Mansion against Zohran Mamdani, New York City's first Muslim mayor.
Balat was captured in photographs and video lighting a small device and throwing it towards the anti-Muslim protesters before lighting a second device handed to him by Kayumi and dropping it, according to a criminal complaint filed in the US district court in Manhattan.
Police were able to intercept the smoking devices - duct-taped jars containing screws and bolts and the explosive substance TATP - and no one was hurt.
After police arrested them, they allegedly said they were inspired by Islamic State, and Balat told police he wanted to carry out an attack "even bigger" than the Boston Marathon bombing in 2013 that killed three people.
Defence lawyer Mehdi Essmidi, who represents Balat, said he was a US-born high school senior of Turkish descent.
"We are actively trying to determine how this came to be and how he came to be in this situation," Essmidi told Reuters.
Mamdani condemned the violence and told reporters he would defend the right of protesters "even when those protesting say things that I abhor".
He and his wife were not home at the time because they had known about the "Stop the Muslim takeover" rally organised by far-right activist Jake Lang more than a week in advance.
More than 100 counter-protesters gathered nearby, the vast majority peaceful, saying they were there to "run Nazis out" of New York.
"While I found this protest appalling, I will not waver in my belief that it should be allowed to happen," Mamdani said of the anti-Muslim rally.
"Let me also be clear about something else: New York City will never tolerate violence, whether from protests or counter-protests."
Lang, who has announced a long-shot bid to represent Florida in the US Senate, told reporters on Saturday he organised the rally because "New York was built by white Christian men" like him, and was "being destroyed by Muslims and socialists".
He brought a goat on a leash to the rally and, with other protesters, dragged around a roasted pig on a trolley, intended as anti-Muslim provocations.
Balat and Kayumi are each charged with five federal crimes, including use of a weapon of mass destruction, and remain in federal custody.
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