PHOENIX, Ariz.—From a plastic chair on the wilting lawn of the State Capitol here, Petra Falcon watches over a makeshift monument that has drawn immigrants worried about the state's tough immigration laws.

A semicircle of American flags surrounds a cluster of candles and statuettes of Jesus and Mary. Before Monday, immigrants had drifted to the arrangement to offer prayers the Supreme Court would overturn the law.

Now, it's attracting people concerned about how the law might affect them.

"It's a growing vigil," said Ms. Falcon, the state director of Promise Arizona, an advocacy group for immigrants that was born out of concern over SB1070, as the law is known. "This community has learned to work together."

On Monday, the Supreme Court struck down many of SB1070's main provisions. But it left in force the most controversial element, which allows police to question people about their immigration status when they are stopped for other reasons. The ruling leaves many immigrants worried and confused about their future.

Immigrant-rights groups such as Promise Arizona launched a flurry of activity across the state in the wake of the ruling. Churches and political groups organized vigils, protests, community forums and legal training sessions. In the next few days, clergy and civil-rights groups are sponsoring forums on the law to help instruct immigrants on how to prepare if they get stopped, and to file complaints if they feel they are being profiled.

Almost immediately after the ruling, a protest sprung up at the Phoenix office of Immigration and Customs Enforcement, the federal agency chiefly responsible for deportations and immigration detentions. Despite 102-degree heat, protesters waved flags and banners outside the ICE office.

"We're going to fight this," shouted one organizer. A national day of protest is scheduled for July 27, when the law is expected to take effect.

Supporters of SB1070 saw the decision as evidence the law was appropriate since its inception in 2010.

Russell Pearce, the former Arizona state senator who drafted SB1070, said the parts of the law that the Supreme Court didn't uphold weren't important to its implementation.

"The parts they didn't uphold were not the meat of the law," Mr. Pearce said in an interview with The Wall Street Journal. "They were the icing on the cake."

The Supreme Court struck down parts of the law that made it a crime for illegal immigrants to seek work and authorized warrantless arrests of people suspected of committing deportable offenses.

Some immigrant advocates agreed the law wouldn't change much for undocumented immigrants.

Magdalena Schwartz, a pastor at a Hispanic church in Mesa, Ariz., said many of the families in her congregation are in the country illegally. But because the families aren't involved in criminal activities, the ruling will allow them to breathe easily.

"God answered our prayers," Ms. Schwartz said. "This is a big victory."

On Monday night, hundreds of immigrants and their families gathered in the auditorium of Carl Hayden High School in Phoenix to ask the city's police chief and mayor questions about how the law will be implemented. City officials attempted to ease fears, telling the crowd in English and Spanish that an inability to speak English wasn't cause for an officer to check immigration status.

Still, much of how the law will work is still unclear. Phoenix Police Chief Daniel Garcia said his department was consulting with lawyers to find out how long an officer could detain somebody while his or her immigration status is checked.

Mayor Greg Stanton told the crowd, "We're studying this carefully. We're going to get this exactly right."

Mr. Stanton opposed the law and appealed to residents of other states not to boycott the state as they had done in the past. "Don't punish small businesses in Arizona because of the acts of the legislature," he said.

But some immigrants in the country illegally worry about the law's potential to split families, particularly in the wake of President Barack Obama's decision last to week to use executive privilege to allow children of illegal immigrants under the age of 30 to stay in the country even though their parents could be subject to deportation.

Neftaly Hernandez, 18 years old, worries her parents could be among them. Ms. Hernandez, who is getting ready to study medicine at Grand Canyon University, was brought illegally to the Phoenix area from Mexico when she was 10.

"I'm so worried about them," Ms. Hernandez said of her parents. "If they left, I would have to leave too."

The ruling also creates uncertainty among business owners.

Todd Landfried, executive director of Arizona Employers for Immigration Reform, said the ruling does nothing to help business owners who grapple with finding and hiring workers legally. His group, which opposed the law, is calling for Congress to take on immigration reform more broadly.

Mr. Landfried said he expects more legal challenges to the part of the law upheld by the Supreme Court, particularly over how it is implemented.

"That constitutional challenge is coming as sure as the sun rises in the east," Mr. Landfried said.

Ms. Falcon, the immigrant-rights advocate, says the Supreme Court ruling isn't the end of the fight, but the start of a new chapter.

"We've still got a lot of questions that need to be answered," she said.

Write to Tamara Audi at and Andrew Morse at