PHOENIX - Hundreds of people supporting Arizona's new law cracking down on illegal immigration rallied Saturday near the state Capitol as temperatures reached 105 degrees.

A procession of motorcycle riders kicked off the downtown Phoenix rally by riding around the Capitol. Supporters waved American flags, and some carried signs that read, "What part of illegal don't they understand?"

The rally's turnout fell far short of the march organized by opponents of the law last weekend, when an estimated 20,000 people gathered.

The group Voice of the People USA, based in Hazleton, Pa., organized Saturday's demonstration, which it touted as a grassroots effort. Attendees traveled from every region of the United States, group president Daniel Smeriglio said.

Demonstrators on Saturday sweated in temperatures predicted to reach as high as 107. Some shaded themselves with umbrellas and clamored to buy cold water and ice cream from vendors.

"For them to come here when it's over 100 degrees and stand in the heat - it's awesome," said Stephanie Colbert, 32, of Glendale.

Colbert and her mother, Pattie Sheahan, 53, of Phoenix, said they strongly supported the new law, which requires that police conducting traffic stops or questioning people about possible legal violations ask about their immigration status if there is "reasonable suspicion" that they are in the country illegally. "Reasonable suspicion" is not defined.

"Everybody needs to obey the same laws," Sheahan said. "If you want to come here, there's ways to do it. Do it the right way."

The law, which takes effect July 29 unless blocked by a court, will also make it a state crime to be in the country illegally or to impede traffic while hiring day laborers, regardless of the worker's immigration status. It would become a crime for illegal immigrants to solicit work.

Critics have said the law will invite racial profiling, whereas supporters have said it will help fight illegal immigration.

Gov. Jan Brewer has ordered a state police training board to prepare training standards to prevent racial profiling in enforcing the law.

Maricopa County Sheriff Joe Arpaio, perhaps best known for his efforts targeting illegal immigrants, drew loud chants of "Joe, Joe, Joe!" from the crowd.

One man yelled to him: "We've got your back, Joe!"

Arpaio praised lawmakers for passing the law and reiterated that he would lock up as many illegal immigrants as his deputies could arrest.

"We'll put tents from here to Mexico," he told the crowd. He was referring to his famed Tent City, a section of the county jail where all inmates are housed in surplus military tents.