WASHINGTON — The Supreme Court considered on Monday whether to allow lawsuits claiming abuse of police power in retaliation for exercising free speech rights. The case concerned a claim for retaliatory arrest at a festival in a remote part of Alaska, but several justices seemed to have an array of controversies in mind.

“You can think of it,” Justice Elena Kagan said, “as a case where an individual police officer, you know, decides to arrest for jaywalking somebody wearing a ‘Black Lives Matter’ T-shirt or, alternatively, a ‘Make America Great Again’ cap.”

Some courts have said the existence of probable cause for the arrest — the person was, after all, jaywalking — is always enough to bar lawsuits claiming retaliation in violation of the First Amendment. Others have allowed juries to decide whether the officers involved intended to suppress protected speech.

The Supreme Court has been struggling to find a line separating two kinds of arrests, Justice Samuel A. Alito Jr. said, noting that “there are a range of cases.”