SAN FRANCISCO—A federal appeals court panel on Thursday grappled with a case that pits data miners’ ability to tap the public portions of the internet for crunchable data with the intersects of large websites that seek to limit access to automated bots.

Former U.S. Solicitor General Donald Verrilli Jr., now a partner at Munger, Tolles & Olson, asked a three-judge panel at the U.S. Court of Appeals for the Ninth Circuit to toss out a lower court’s injunction against his client LinkedIn Corp. A federal judge in San Francisco late last year issued a preliminary injunction barring LinkedIn from blocking data analytics company hiQ Labs from accessing the public profile information of LinkedIn users.