Two of Wal-Mart Stores Inc.’s most vocal critics — the United Food and Commercial Workers International Union, which backs WakeUpWalmart.com, and Wal-Mart Watch — are putting pressure on the world’s largest retailer to disclose if it has monitored its workers’ communications.

The moves come amid a federal investigation after Wal-Mart said a systems technician monitored text messages and phone calls of other employees and non-employees, including a New York Times reporter. In a conference call with reporters Monday afternoon, Wal-Mart spokeswoman Mona Williams said the technician “acted alone” and used his own personal equipment to intercept text and pager messages.