WASHINGTON — Most Jewish groups who have weighed in on Arizona’s controversial immigration law saw progress in the U.S. Supreme Court’s ruling to repeal three of the law’s four parts, but had concerns that law enforcement officials would still be allowed to check the legal immigration status of people they detain.

The high court on Monday invalidated the provisions authorizing police to arrest illegal immigrants without warrant if there was probable cause that they committed an offense that made them eligible for deportation; making it an Arizona state crime if immigrants did not carry registration papers or some sort of government identification; and forbidding immigrants unauthorized to work in the country to apply, solicit or perform work.

The Hebrew Immigrant Aid Society was among the groups that welcomed the repeals but had reservations with the decision.

“Though we view the positive part of this ruling as another step in the advancement of immigrant rights — forwarded recently by President Obama’s executive order halting deportations of Dream Act eligible individuals — we remain extremely concerned about the potential for racial profiling as a result of today’s decision,” Mark Hetfield, the interim president and CEO of HIAS, said in a news statement.

The law, passed in April 2010, was meant primarily to deal with illegal immigrants coming from Mexico, according to proponents of the measure at the time of its passage. They also noted that Arizona Gov. Jan Brewer had issued an executive order establishing a training program on how to avoid racial profiling when implementing the new rules.

In April, HIAS coordinated a letter to Brewer, a Republican, and also joined more than 100 other faith-based organizations and civil rights groups in submitting an amicus brief that urged the Supreme Court to strike down Arizona’s law.

Anti-Defamation League national director Abraham Foxman and national chair Robert Sugarman in a news statement called the ruling a “mixed outcome.”

“One of our primary concerns has been that Arizona’s law would exacerbate fear in immigrant communities and, in particular, make victims and witnesses of hate crimes reluctant to speak with police,” they wrote.

“We urge Arizona and the lower courts to endorse the principle that all women, men and children deserve equal protection under the law, as appearance offers no grounds on which to assume the legal status of an individual,” Saperstein wrote. “Engaging in racial profiling only jeopardizes the safety of entire communities, as members of immigrant communities fearful of being profiled are discouraged from cooperating with law enforcement on issues.”