"That's the fuel that motivated them to come here, because of the sadness of the Arizona law," he said.
In Los Angeles, an estimated 60,000 people joined a march through the city's downtown area, many waving US flags.
Campaigners calling for changes to federal immigration laws have seen a rise of activity since the Arizona measure was passed.
Activists have urged a boycott of Arizona businesses and organised protests outside Arizona Diamondbacks baseball games.
"I don't really believe that this law is going to do what the vast majority of Americans and Arizonans want, and that is to fix the immigration problem"
Phoenix police chief
"What happened in Arizona proves that racism and anti-immigrant hysteria across the country still exists. We need to continue to fight," Lee Siu Hin, a co-ordinator with the Washington, DC-based National Immigrant Solidarity Network, said.
Barack Obama, the US president, had promised to tackle immigration reform in his first 100 days in office, but has pushed back that timetable several times.
He said earlier this week that Congress may lack the "appetite" to take on immigrationafter going through a tough legislative year.
Al Jazeera's Cath Turner, reporting from Arizona state capital Phoenix, said that many critics see the Arizona law as "simply an excuse for racial profiling".
"The Hispanic community and human rights groups say this will simply mean that Hispanics are targeted," she said.
"No other racial group would be suspected of being in Arizona illegally when the US state is so close to the Mexican border."
Arizona officials have denied the accusations, saying that the law forbids racial profiling.
However, the concerns led to the language being changed and a new version of the law that explicitly bars officers using race as a reason to question suspects and requires scrutiny of people who police stop, detain or arrest.
"These changes specifically answer legal questions raised by some who expressed fears that the original law would somehow allow or lead to racial profiling," Brewer said in a statement.
"These new amendments make it crystal clear and undeniable that racial profiling is illegal and will not be tolerated in Arizona."
But Jack Harris, the police chief of Phoenix, said on Friday that the legislation would likely create more problems than it solved for officers.
"I don't really believe that this law is going to do what the vast majority of Americans and Arizonans want, and that is to fix the immigration problem ... This law adds new problems for local law enforcement," he said.
"We have the tools that we need to enforce the laws in this state, to reduce property crime and reduce violent crime, to go after criminals that are responsible for human smuggling," and other border-related crimes."
Backers have said that the law is needed to curb crime in the desert state, which is home to an estimated 460,000 illegal immigrants and is used by drug and people traffickers operating from Mexico.