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.
"An attack on one is an attack on all, and New York stands in solidarity with the British people and our friends around the world against the forces of hate and terror," he said.
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.
Police said at least 19 people were killed and around 50 were wounded in the attack just as Grande left the stage.
It is the deadliest attack in Britain since 2005.
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