From the World Trade Center and Times Square in New York to the White House and sports venues across the country, police patrolled in packs and deployed counterterrorism teams Monday as security was stepped up after explosions at the Boston Marathon.

Worries also reverberated across the Atlantic, where an already robust security operation was being beefed up for Wednesday’s ceremonial funeral for former Prime Minister Margaret Thatcher. The event at St. Paul’s Cathedral, to be attended by Queen Elizabeth II and other dignitaries, calls for a procession through the streets of London, with Thatcher’s flag-draped coffin carried on a horse-drawn carriage.

British police were also reviewing security plans for Sunday’s London Marathon — the next major international race — because of the bombs that killed three people and injured more than 140 in Boston.

Across the United States, security was tightened at landmarks, government buildings, transit hubs and sporting events. Law enforcement agencies also urged the public via Twitter and Facebook to report suspicious activity to the police.

In New York, authorities deployed so-called critical response teams — highly visible patrol units that move in packs with lights and sirens — along with more than 1,000 counterterrorism officers. Highly trafficked areas such as the Empire State Building, Rockefeller Center, St. Patrick’s Cathedral, the United Nations and the World Trade Center site were being especially monitored.

Mayor Michael Bloomberg said the police department was fully prepared to protect the city.

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“Some of the security steps we are taking may be noticeable,” Bloomberg said. “And others will not be.”

In Washington, Secretary of Homeland Security Janet Napolitano urged the American public “to be vigilant and to listen to directions from state and local officials.”

“At the president’s direction, the Department of Homeland Security is providing any support necessary in this ongoing investigation,” she said.

At the White House, the Secret Service expanded its security perimeter after the attacks, shutting down Pennsylvania Avenue and cordoning off the area with yellow police tape. Secret Service patrol cars blocked off entry points, although the White House was not on lockdown and tourists and other onlookers were still allowed in the park across the street.

Speaking late Wednesday from the White House, President Obama declared that those responsible would “feel the full weight of justice,” although he urged a nervous nation not to jump to conclusions and pointedly avoided using the words “terror” or “terrorism.”

However, top lawmakers declared the deadly incident an act of terrorism, and a White House official said it was being treated that way.

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Police in Los Angeles, Washington, San Diego, Las Vegas, Detroit, Atlanta and other major cities were monitoring events closely and assessing increases in security measures.

In California, emergency management officials activated their statewide threat assessment system, which was established after the Sept. 11 attacks. And officials in multiple cities and counties throughout the state were reviewing information from federal authorities for possible threats.

In Seattle, police increased patrols in neighborhoods and around government buildings and other facilities. In Colorado, a statewide alert was sent out advising law enforcement agencies to look out for suspicious activities.

In New Jersey, authorities raised security statewide, calling in off-duty state police officers and deploying bomb units, aviation crews, tactical teams and search and rescue assets as a precaution.

Transit and port officials in New York and New Jersey were on heightened alert at bridges, tunnels and on rail lines between the two states, as well as on New York City’s subway system and commuter rails.

And at the Port of Los Angeles and Long Beach, as well as at three major Los Angeles airports, including Los Angeles International, law enforcement officials were in a “heightened state of vigilance,” with increased patrols, authorities said.

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Security was also tightened at sports venues nationwide, though most events were held as planned. The postponement of Monday night’s NHL game between the Bruins and Ottawa Senators, and the cancellation of Tuesday’s NBA game between the Celtics and Indiana Pacers — both events to be held in Boston — were the most tangible reactions by sports officials to the explosions.

Still, officials announced plans for security reviews of upcoming marathons and road races in cities large and small, including this weekend’s marathon in Lansing, Mich., Nashville’s Country Music Marathon on April 27, next month’s Indianapolis 500 Festival Mini-Marathon and the San Francisco Marathon in June.

Race officials for the Illinois Marathon in Champaign and Urbana, Ill., said they were already fielding calls from worried runners and their families and planned to meet Wednesday to discuss more security measures such as bomb-sniffing dogs.

“I took a call from a very irate parent who screamed at me because I won’t cancel the race, because I’m putting her daughter at risk,” said Jan Seeley, a director for the Illinois Marathon. “And we’re anticipating more of that.”

Even so, life went on as usual in locations across the country. In New York’s Times Square, tourists crowded the sidewalks seemingly unconcerned about any possible heightened risk. One area was being emptied — but for a movie shoot, not for security, as helicopters buzzed overhead.

Shelly Bybee, 42, a teacher visiting from Austin, Texas, said the idea of public safety was more on her mind, 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.”