President Barack Obama also , saying it could lead to harassment of Hispanics, and he called for bipartisan support to fix America's broken immigration system. Two senior officials in his government said the Arizona law may face a legal challenge by federal authorities.
"Now suddenly if you don't have your papers, and you took your kid out to get ice cream, you're going to get harassed - that's something that could potentially happen," the U.S. president said of the measure. "That's not the right way to go."
Arizona's law - slated to take effect in late July or early August - makes it a state crime to be in the U.S. illegally and allows police to question anyone they suspect of being an illegal immigrant. Lawmakers said the legislation, which has and litigation, was needed because the Obama administration is failing to enforce existing federal laws.
Mexico's Foreign Ministry issued a travel alert for Arizona after the law was signed, warning that its passage shows "an adverse political atmosphere for migrant communities and for all Mexican visitors."
The alert said that once the law takes effect, foreigners can be questioned at any moment and detained if they fail to carry immigration documents. And it warns that the law will also make it illegal to hire or be hired from a vehicle stopped on the street.
A Mexican government-affiliated agency that supports Mexicans living and working in the United States called for boycotts of Tempe, Ariz.-based US Airways, the Arizona Diamondbacks and the Phoenix Suns until those organizations rebuke the law.
"We are making a strong call to the Arizona government to retract this regressive and racist law that's impacting not only residents of Arizona, but people in all 50 states and in Mexico as well," said Raul Murillo, who works with the Institute for Mexicans Abroad, an autonomous agency of Mexico's Foreign Ministry.
US Airways spokesman Jim Olson said "we have had absolutely no customers who have canceled flights" as a result of the controversy. Calls to the Diamondbacks and the Suns were not immediately returned.
In Washington, Attorney General Eric Holder and Homeland Security Secretary Janet Napolitano criticized the law, with Holder saying the .
A number of options are under consideration, including "the possibility of a court challenge," Holder said.
A also is expected. Jon Garrido, who produces a Hispanic website and ran unsuccessfully last year for the Phoenix City Council, said he plans to begin gathering signatures next week to get a repeal referendum on the November ballot. If successful, the effort would block the law from taking effect until the vote.
Obama said Tuesday that "poorly conceived" measures such as Arizona's can be halted if the federal government fixes the U.S. immigration system for good.
Obama pledged to bring his own party along, pleading with Republicans to join in as the only realistic hope to solve a politically volatile problem and get an immigration deal done.
"I will bring the majority of Democrats to the table in getting this done," Obama said in response to a question at a town hall in south-central Iowa. "But I've got to have some help from the other side."
U.S. politicians also weighed in on the growing controversy, with election season looming.
In California, Meg Whitman, the Republican front-runner in the California gubernatorial primary, said Arizona is taking the wrong approach.
"I think there's just better ways to solve this problem," Whitman said in a telephone interview with The Associated Press.
California state Sen. President Pro Tem Darrell Steinberg said the law attempts to legalize racial profiling and called on Gov. Arnold Schwarzenegger to review the state's contracts with Arizona and cancel them if legally possible.
Schwarzenegger has not yet replied, but told reporters that immigration matters are the responsibility of the federal government.
Arizona Sen. John McCain, seeking re-election, told CBS' "The Early Show" that his state needed such a law because the Obama administration has failed to secure the borders, resulting in drugs pouring into the southwestern United States from Mexico.
McCain on Immigration Law
Each day, more than 65,000 Mexican residents are in Arizona to work, visit friends and relatives and shop, according to a University of Arizona study sponsored by the Arizona Office of Tourism. While there, the Mexican visitors spend more than $7.35 million daily in Arizona's stores, restaurants, hotels and other businesses, the researchers found.
Bimbo Bakeries, one of many Mexican companies operating in Arizona, said Tuesday it doesn't expect Arizona's new immigration law to affect its employees.
"We carefully screen all associates to ensure they are authorized to work in the United States," Bimbo spokesman David Margulies said.
At the Mexico City airport Tuesday, Mexicans heading for the U.S. said they were very troubled by the new law.
"It's humiliating," said Modesto Perez, who lives in Illinois. "It's really ugly."