NEW YORK  — The New York Police Department stepped up security at hotels and landmark locations like the World Trade Center site, Empire State Building and Times Square on Monday following explosions at the Boston Marathon.

While officials said there was no report of a specific threat to New York, Mayor Michael Bloomberg urged city residents to be vigilant as police took both highly visible and unseen precautions.

Critical response teams, which are patrol units that travel in packs with lights and sirens, are being deployed throughout the city until more about the explosion is learned, chief police spokesman Paul Browne said.

“We anticipate keeping a robust presence in place until we learn more,” Browne said. “There’s a high level of concern about what happened in Boston.”

More than 1,000 counterterrorism officers were mobilized, along with the thousands of other officers on patrol. Highly trafficked areas like Times Square, Rockefeller Center and St. Patrick’s Cathedral in Midtown Manhattan, the United Nations, and the World Trade Center site were being especially monitored, police said.

Times Square teemed as usual, with tourists seemingly unconcerned about any possible heightened risk. One area was being emptied — but for a movie shoot, not for security. Helicopters buzzed overhead.

Shelly Bybee, 42, a teacher from Austin, Texas, said the idea of public safety is more on her mind when she is in a large public space than when she isn’t, and particularly in New York, given the Sept. 11 attacks.

But, “that was on my mind even before I heard about the explosion in Boston,” she said. Overall, “I feel like we should continue living and go about our business.”

Gov. Andrew Cuomo directed the state division of homeland security and emergency services to be on heightened alert.

Security was also beefed up within the subways. The Metropolitan Transportation Authority said it was also stepping up patrols on the Long Island Rail Road and Metro North commuter rails. Bags may be searched.

“There’s nothing we know that we think is going to happen, but we have to be prepared,” Bloomberg said at an unrelated evening event.

“We are asking all New Yorkers to remain vigilant in the days ahead” and call authorities if they see anything that seems suspicious, said Bloomberg, who took office in the wake of the Sept. 11 attacks. “But at the same time, we refuse to let cowardly acts of violence stop us from living in our city.”

The blasts occurred at the finish line of the marathon. The explosions have killed at least three people and injured at least 130 others. The cause wasn’t known.

The New York Road Runners, operators of the ING New York City Marathon that was canceled last November following Superstorm Sandy, said security was their top priority.

“We will continue to work hand in hand with the City of New York and the NYPD as we plan for upcoming events,” they said in a statement.

The NYPD regularly steps up security in the city as a precaution based on incidents in other locations.

Maria Martone, 45, of Cape Cod, Mass, was visiting New York with husband Michael, 50; their daughter, Miranda, 15, and a teen friend of Miranda’s.

Michael Martone said that if the point of the explosions was to frighten people “you’ve got to resist as much as you can.”