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About 30 protesters have been arrested on Tuesday around Manhattan in a day of May Day demonstrations organized by Occupy Wall Street, the police said.

Most of the arrests were on disorderly conduct charges, but some people were charged with assault, the police said. And some demonstrators who tried to avoid being detained on various charges were charged with resisting arrest, the police said. Protesters were arrested near Bryant Park in Midtown, on the Williamsburg Bridge, at a park on the Lower East Side and near Washington Square Park as marchers kept on the move and repeatedly converged and split off.

Around 3 p.m., a crowd surged out of Washington Square Park carrying a banner that read “On Strike.” Officers shouted for protesters to remain on the sidewalk, but several protesters holding the banner stepped into the middle of Avenue of the Americas, where several officers — including one in plain clothes who had appeared to be marching with the crowd — tackled and arrested them.

One protester who was led away in cuffs had a bloodied face.

Breaking News Network, which transcribes emergency radio broadcasts, reported six arrests at the clash near Washington Square Park.

Activists and the police had been playing cat-and-mouse across downtown, as the marchers ranged quickly from Chinatown to SoHo to Greenwich Village, taking to the roadways and often moving against traffic apparently in an attempt to thwart pursuit.

At a rally in Union Square, where protesters were gathering around 3:15, the themes were the ones that Occupy Wall Street has sounded from the outset of the movement last fall — opposition to big banks and the government that bailed them out after they helped cause the recession.

“I just watched the whole economy becoming devastating, and no one wants to hire me,” Kenzia Snyder, 59, a freelance chef from Chelsea, said at Union Square. “There are so many issues that are all coming together. It’s shameful how the powers are abusing the 99 percent.”

The May Day demonstrations took place across the United States and around the globe.

In the Bay Area in California, marches and protests snarled traffic and caused road closings. Hundreds marched through Oakland, temporarily closing streets and bank branches and clashing with officers in riot gear, who deployed tear gas on crowds.

The Golden Gate Ferry service, used by many commuters from Marin County to San Francisco, was shut down after workers in bitter contract negotiations over health insurance coverage went on strike and picketed ferry terminals.

On Monday night, protesters had marched through San Francisco’s Mission District, throwing paint and smashing storefront windows at dozens of businesses, restaurants and the local police station. The group also vandalized parked cars, broke windows and spray painted anarchy symbols on car hoods.

In New York on Tuesday, about 1:30 p.m. a few hundred protesters who had assembled on the Lower East Side at Sara D. Roosevelt Park began heading east, crossing Forsyth Street. They were met by a line of police officers who pushed them back, grabbed people out of the crowd, threw them to the ground and arrested at least four of them while trying to wrest a large banner away from the marchers.

Officers then plunged into the crowd that was gathered on the south side of Houston Street, at the north end of the park, pushing protesters and journalists alike and making further arrests. The crowd took off running south through the park and east onto Forsyth Street.

The Metropolitan Transportation Authority issued an alert in the afternoon that “as a result of today’s May Day demonstrations, bus detours may be necessary along several routes traveling through Lower Manhattan” and that subways might be extra crowded. “Customers heading home during the afternoon/evening rush are urged to plan for extra travel time,” the agency said.

As of 12:30 p.m. hundreds of protesters from several converging marches had formed a “picket line” on East 42nd Street and were marching back and forth in front of a Wells Fargo branch and the Capital Grille restaurant, part of a chain that is the subject of a class-action suit alleging wage theft and discrimination. The protesters filled the whole block on the north side of 42nd Street between Lexington and Third Avenues.

Protesters were also gathering downtown at Sara D. Roosevelt Park at Chrystie and Houston Streets.

On a rain-dampened morning, the widespread May Day protests coordinated by Occupy Wall Street got off to a relatively slow and calm start in New York, but by 11 a.m. Tuesday, many hundreds of protesters had massed in Bryant Park under the watchful eye of the police and private security.

Earlier, small bands of protesters spread out around Midtown, often moving quickly from place to place, and forming picket lines in front of buildings connected to certain companies. Shortly before 9 a.m., several dozen people walked back and forth in front of the Bank of America tower at 42nd Street and Avenue of the Americas chanting, “Bank of America, hey hey, who did you foreclose today?”

“This is one of the most screwed-up companies in America,” said one protester, Zeke Dunn, 30, a film and television producer from Greenpoint, Brooklyn. “They got a $41 billion safety net, and the rest of us got nothing.”

Another group, with about 20 protesters, marched through the center of Grand Central Terminal blowing bullhorns and chanting, “We are unstoppable, another world is possible.”

Protesters carrying placards denouncing corporate greed very briefly blocked Fifth Avenue – for about 15 seconds – and were moved along by officers. At another point, a man was led off in handcuffs after witnesses said he stopped while crossing a street in Midtown and would not move.

Protesters also formed picket lines outside of several buildings housing Chase Manhattan bank offices. Thirty blocks south, in Union Square, protesters numbered in the handful and were far outnumbered by the police.

By 11 a.m., several hundred people who had been assembled on the western edge of Bryant Park were joined by hundreds of others who came streaming in from 42nd Street after participating in various marches.

They assembled on the western part of the park near a large fountain, where a marching band played and drummers pounded out a beat. Private security guards and city police officers also gathered, standing in small groups nearby and watching the crowd.

Read this version of the story for additional detail.

Daniel Krieger in Manhattan and Malia Wollan in Oakland contributed reporting .