Rev. Jesse Jackson, right, and demonstrators march during a May Day rally in Chicago. Hundreds of thousands of people rallied across the United States. (Nam Y. Huh/Associated Press)

Hundreds of thousands of people demonstrated Saturday in more than 70 cities across the United States against a controversial new immigration law in Arizona.

Rallies have already been held to denounce the measure since it was signed by Arizona Gov. Jan Brewer last week, but Saturday's marches, coinciding with traditional May 1 events around the world, were by far the largest the United States has seen so far in response to the legislation.

Dozens of prominent political, media and religious figures decried the law in protests in cities like Los Angeles, Dallas, Chicago, Phoenix, Washington, Boston and New York.

"It's the right of every American to protect where they live," Cuban-American singer Gloria Estefan said in Spanish at the L.A. rally. "But that's not a reason to enact a law that could create racism and discrimination."

Catholic Cardinal Roger Mahony of Los Angeles, centre (in black), marches arm-in-arm Saturday with demonstrators rallying for reform of U.S. immigration laws and to protest Arizona's new immigration law. (Chris Carlson/Associated Press)

The Catholic cardinal of L.A., Roger Mahony, joined the demonstration of 100,000 people, chanting "Si, se puede," or "Yes, we can," from atop a flatbed truck.

Marchers wore T-shirts saying "Boycott Arizona" and held up banners reading "Overturn Arizona Apartheid."

In New York, labour organizer John Delgado said anger over the law drew thousands of people to a rally.

"She's awakened a sleeping giant," Delgado said, referring to Brewer.

Congressman arrested

Illinois Representative Luis Gutierrez, a Democrat, was arrested with about 35 other people after they staged a sit-in in front of the White House in Washington, chanting "Si, se puede."

Thousands of marchers also turned out in Boston and in Chicago, where protests greeted the Arizona Diamondbacks at a baseball game earlier this week.

The countrywide rallies echoed demonstrations four years ago across the U.S., when more than a million people united to protest ultimately unsuccessful federal legislation that would have made being a non-status immigrant a felony.

"What happened in Arizona proves that racism and anti-immigrant hysteria across the country still exists. We need to continue to fight," said Lee Siu Hin, a co-ordinator with the Washington, D.C.-based National Immigrant Solidarity Network.

Arizona's strict new immigration law, which goes into effect July 29 barring a court challenge or a state referendum to repeal it, requires local and state law enforcement to question people about their immigration status if there's reason to suspect they're in the country without proper documentation, and makes it a state crime to be in the United States illegally.

Opponents say the law is unconstitutional for a host of reasons and will exacerbate racial profiling by police, who will be statutorily obliged to interrogate anyone who looks like an immigrant.

Demonstrators also want U.S. President Barack Obama to fulfil his promise for comprehensive reform of the country's immigration system. Estimates suggest about 11 million non-documented immigrants live in the U.S., the majority of whom work and pay sales taxes but don't receive government benefits.

May 1, or May Day, is the traditional Labour Day in many countries around the world, where rallies are held for a variety of social-justice causes.

With files from The Associated Press