PHOENIX, Nov 10 (Reuters) - Large firms that pose risks to the financial system as a whole should face higher capital requirements and tighter supervision, San Francisco Federal Reserve Bank President Janet Yellen said on Tuesday.

However, she said she disagreed with former Fed Chairman Alan Greenspan and Bank of England Governor Mervyn King, who have argued that banks that are considered too big to fail are simply too large to exist.

Instead, these institutions should pay a premium, she said.

"They should pay a penalty for the risk they create," Yellen said.

(Reporting by Pedro Nicolaci da Costa, Editing by Chizu Nomiyama)