In a case that could sharpen the law around arbitration contracts used by apps and websites, judges from the U.S. Court of Appeals for the Second Circuit are considering whether to sign off on an arbitration agreement that Uber Technologies Inc. wrapped into the terms of service for individuals who use the app to seek rides.

At least one judge said the agreement would have been strengthened if Uber had required users to click a button expressly agreeing to the terms. However, the panel also appeared dubious on March 24 that the plaintiff in a price-fixing lawsuit against Uber could have been unaware that he was entering into a contract with the company when signing up for its ride-hailing app.