WASHINGTON (Reuters) - President Barack Obama on Thursday nominated former federal prosecutor Mary Jo White to head the Securities and Exchange Commission, signaling a desire for tough oversight of Wall Street.

Obama also renominated Richard Cordray to continue as the head of the Consumer Financial Protection Bureau, the U.S. watchdog for consumer products such as mortgages and student loans.

Obama told a White House ceremony that there is more work needed to confront what he called irresponsible behavior in the Wall Street financial sector and that White would have this duty.

(Reporting by Steve Holland and Matt Spetalnick; Editing by Will Dunham)