Senior police officers in Arizona have warned that their relations with Hispanic communities could be damaged after the US supreme court allowed a section of the state's hardline immigration law to stand.

The provision, dubbed the "show me your papers" clause, requires that officers check the immigration status of anyone they "reasonably suspect" of being present illegally in the US.

US supreme court justices allowed the measure to stand on Monday, when they struck down other aspects of Arizona's draconian anti-immigration laws.

Roberto Villasenor, the chief of police of Arizona's second largest city, Tucson, warned that the supreme court was taking the police into dangerous new territory. He said no case law existed that gave clear guidance on how officers should interpret the "reasonable suspicion" clause – a term that is not defined in the text of the legislation.

"Under the supreme court decision, police departments in Arizona must enforce section 2b, and no one respects the authority of the courts more than police chiefs, so we will do our best to enforce the law. But we are in uncharted territory on this issue," Villasenor said.

He also warned that it exposed the police to the threat of multiple legal actions from the public. Under the wording of the law, public individuals are given the power to sue the police if they think the provisions of the act are not being fulfilled. "So police in Arizona may be sued by people who believe they are not aggressive enough in enforcing the law – or by others who believe that police are being too aggressive or are engaging in racial profiling," he said.

By a majority of five to three, the court blocked implementation of several components of the SB1070 law on the grounds that the federal government had broad powers for setting immigration policy, not individual states.

The Obama administration had wanted the whole Arizona immigration law declared unconstitutional.

Justices did not come out in favour of the police power, simply saying it was withholding its view until lower courts discussed it. It said that "without the benefit of a definitive interpretation from the state courts, it would be inappropriate to assume [the police power] will be construed in a way that conflicts with federal law".

Arizona's Republican governor, Jan Brewer, who introduced the law on the grounds that the state was having to act because of the failure of the federal government to act, said the ruling was a victory because it left in place the measure at the "heart" of the legislation.

Other police chiefs also sounded the alarm, speaking through their national umbrella organization, the Police Executive Research Forum. William Lansdowne, police chief for the Californian city of San Diego, described giving the public the power to sue as a "recipe for trouble. This kind of provision could jam up the courts and cost police departments and cities a fortune".

Police chiefs in Arizona have long been anxious about the impact that the new law would have on their abilities to function. In 2010, when SB1070 was enacted, the Arizona Association of Chiefs of Police put out a statement (pdf) saying "the provisions of the bill remain problematic and will negatively affect the ability of law enforcement agencies across the state to fulfill their many responsibilities in a timely manner".

In March, more than a dozen chiefs wrote a brief to the supreme court before this week's decision arguing that police officers would find it impossible to determine whether there was a "reasonable suspicion" that an individual they came in contact with might be undocumented. The chiefs, who included Villasenor and two other law enforcers from Arizona, pointed out that 50 million individuals are lawfully admitted into the US every year and to be able to discern them apart from those illegal entrants would require police officers to be skilled in the intricacies of immigration law.

"As a result, Arizona police officers would be inevitably impelled to presume that virtually all those they stop or arrest are unlawfully present in the US," the brief said.

It will take weeks or even months for the finer implications of the supreme court ruling to become clear, as police, immigration officers, civil rights groups and Latino organizations in Arizona begin to sift through its complex message. One big consideration that will also become clearer over time is to what extent the ruling will effect other states which are keen to follow Arizona's example and crack down on illegal immigration.

Several states, including Alabama, Georgia, South Carolina and Virginia have considered introducing variations on the theme of SB1070, adopting its guiding principle of "attrition through enforcement". That seeks to make life in American cities so uncomfortable for undocumented immigrants that they chose to leave the country of their own volition, a concept that the presumptive Republican candidate Mitt Romney embraced under the rubric "self-deportation".

Civil rights groups are prepared for mission creep – the sense that by allowing the "reasonable suspicion" clause to stand in Arizona the supreme court may encourage other states to copy it. The ACLU, that is leading legislative challenges to the Arizona law, has amassed what it calls an $8.7m war chest to litigate against any and every state that attempts to pass new laws that seek to criminalise the presence of undocumented immigrants and thus bring them into the purview of the police.

"If you are a state that wants to try to enact these laws, we will see you in court," said Anthony Romero, ACLU's executive director.

In a statement, Obama said: "I am pleased that the supreme court has struck down key provisions of Arizona's immigration law. What this decision makes unmistakably clear is that Congress must act on comprehensive immigration reform. A patchwork of state laws is not a solution to our broken immigration system – it's part of the problem.

"At the same time, I remain concerned about the practical impact of the remaining provision of the Arizona law that requires local law enforcement officials to check the immigration status of anyone they even suspect to be here illegally. I agree with the court that individuals cannot be detained solely to verify their immigration status."

Romney, who is visiting Arizona on Monday and will almost certainly be asked out the ruling, released a statement after the ruling. "I believe that each state has the duty – and the right – to secure our borders and preserve the rule of law, particularly when the federal government has failed to meet its responsibilities. As candidate Obama, he promised to present an immigration plan during his first year in office. But four years later, we are still waiting."