U.S. financial markets should have a backup system that consolidates stock quotes for the nation's trading exchanges, Nasdaq CEO Robert Greifeld said Friday — a day after a problem with the current system paralyzed trading in Nasdaq-listed stocks for three hours.

"I certainly couldn't argue against that," Greifeld told CNBC in an interview before financial markets opened.

Nasdaq is in charge of consolidating and disseminating the National Best Bid and Offer for Nasdaq-listed stocks such as Apple and Microsoft. Nasdaq transmits those quotes to the 13 U.S. trading exchanges.