KEY POINTS
  • Cleveland Fed President Loretta Mester called May's job gains "solid," but said more progress is needed.
  • Payrolls rose by 559,000 for the month, but Mester said the labor market still has more room to recover.

May's job gains were "solid" but not enough to change the direction of monetary policy, Cleveland Fed President Loretta Mester told CNBC.

"Bottom line, I would like to see further progress than where we are right now," Mester told CNBC's Steve Liesman during a live "Squawk on the Street" interview Friday.