Passengers on several cruise lines have tested positive for the new coronavirus in recent days, complicating efforts by the industry to suspend its operations and return 90,000 passengers still at sea.

One British cruise ship is asking Cuba to allow it to dock after other Caribbean islands denied it entry because it has a coronavirus outbreak. Several Carnival Corp. and Royal Caribbean Cruises Ltd. boats have stopped in places such as Brazil, the Canary Islands or Puerto Rico to drop off passengers who tested positive for...