New York Governor Andrew Cuomo said he was ordering additional patrols at "high-profile locations" including airports and the subway "out of an abundance of caution" after the assault at the show by US pop star Ariana Grande.
"This apparent act of terrorism, targeting a concert attended by thousands of teenagers and young people, is an inexplicable and abhorrent assault on our universal values as human beings," Cuomo said in a statement.
The US Department of Homeland Security said it was working to find information and stood ready to assist counterparts in Britain.
"At this time, we have no information to indicate a specific credible threat involving music venues in the United States," the department said in a statement.
"However, the public may experience increased security in and around public places and events as officials take additional precautions," it said.
It is the deadliest attack in Britain since 2005.
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