(CNN) -- Thousands of protesters in cities across the United States waved American flags as they rallied Saturday against Arizona's tough new immigration law and pushed for national immigration reform.





"Si se puede," "Yes we can" and "Boycott Arizona" were common refrains for groups protesting from Los Angeles, California, to New York City.





May 1 is traditionally a rallying day for supporters of immigration reform. But protesters across the country said they were galvanized by Arizona's recent passage of a law cracking down on illegal immigration.





The new Arizona law requires immigrants to carry their alien registration documents at all times and requires police to question people if there is reason to suspect they are in the United States illegally. Critics say it will lead to discrimination and racial profiling.





But Arizona Gov. Jan Brewer has said the law is necessary because the federal government has failed to enforce border security with Mexico, allowing hundreds of thousands of illegal immigrants to move into the state. She said changes to the law she approved Friday, which clarify that police could only stop suspected illegal immigrants while enforcing some other law or ordinance, should eliminate concerns about racial profiling.





But criticism of the law was clear among tens of thousands of protesters flooding the streets of Los Angeles on Saturday, where organizers said they hoped to send a strong message with the number of people turning out.





"Does my face look illegal?" one sign read.





Karen Rayner, a spokeswoman for the Los Angeles Police Department, said 50,000 people marched at the demonstration's peak. Rayner said the rally was "very peaceful" and no one was arrested.





Police arrested about 20 protesters -- including a U.S. congressman -- at Saturday's rally in Washington.





Rep. Luis Gutierrez, D-Illinois, was among a group of protesters who were arrested for blocking the sidewalk outside the White House in what they said was a planned act of civil disobedience. The protesters wore T-shirts that read "ARREST ME NOT MY FAMILY" and "ARREST ME NOT MY FRIENDS."





A smaller group of about 200 people rallied outside the State Capitol in Phoenix, protesting the new law and asking the federal government to step in to stop it.





About 1,000 people gathered in New York City's Union Square on Saturday afternoon.





Cesar Mack, an international studies student at City College of New York, told CNN he was an undocumented immigrant from Peru.





"I've been living in this country six years and I'm still fighting for immigration reform," he said.





CNN iReporter Julio Ortiz-Teissonniere said he saw signs in Arabic, French, Spanish and English at the New York rally. One sign in the crowd particularly caught his eye: "Todos somos Arizona" -- "We are all Arizona."





"They were trying to convey that message that it's a city and nation based on immigration. Everybody came from somewhere else," he said.





CNN's Susan Candiotti, Ted Rowlands, Ione Molinares and Casey Wian contributed to this report.
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question: who was arrested during a rally, answer: Rep. Luis Gutierrez, | question: How many people gathered in New York City's Union Square on Saturday afternoon?, answer: 1,000 | question: Where were rallies held, answer: cities across the United States | question: What were Gutierrez and other protesting?, answer: Arizona's tough new immigration law | question: Where was Gutierrez and others protesting?, answer: sidewalk outside the White House | question: Who was arrested during a rally in Washington?, answer: Rep. Luis Gutierrez, | question: how many people gathered, answer: Thousands