Executives from Target Corp. and Neiman Marcus Group Ltd. on Tuesday pledged to work with Congress to better protect consumer information, as they made their first public appearances on Capitol Hill to discuss their companies’ recent data breaches.

John Mulligan, the executive vice president and chief financial officer of Target, and Michael Kingston, the senior vice president and chief information officer of Neiman Marcus, told members of the Senate Judiciary Committee that their companies have offered free credit monitoring and taken other steps to help customers whose data hackers may have targeted. But the executives said they also would support efforts by others to make credit and debit card transactions safer.