In a series of meetings with his Las Vegas casino personnel in recent days, casino mogul Steve Wynn urged employees to rally to his side following sexual-misconduct allegations against him, according to audio recordings of the meetings made by participants.

Mr. Wynn, the chairman and chief executive of Wynn Resorts Ltd., didn’t directly address the allegations against him, according to the recordings reviewed by The Wall Street Journal. Instead, he stressed that he considers his employees a “family.” In difficult financial...