Federal Reserve Chairman Ben Bernanke said on Friday that the shadow banking system continued to pose a threat to financial stability, and that bank funding markets might still not be able to cope with a major default.

In a wide-ranging speech explaining the Fed's role in monitoring the stability of the banking system, Bernanke also said the central bank was closely monitoring asset markets for signs of excessive risk taking.

"While the shadow banking sector is smaller today than before the crisis ... regulators and the private sector need to address remaining vulnerabilities," Bernanke said in the text of a speech due for delivery in Chicago.

More work was needed to ensure the repo market - the wholesale market banks use for their everyday funding needs - could deal with the potential consequences of a default by a large borrower or a broker-dealer.

And a run on money market funds also still remained a possibility, Bernanke said.

Bernanke said the Fed was monitoring a wide range of asset markets for signs investors were "reaching for yield" in a way that might pose risks to the financial system, given that interest rates were so low.

Bernanke did not address the outlook for monetary policy or the economy, nor did he discuss remarks by Fed Governor Daniel Tarullo last week that current globally agreed limits on how much banks can borrow might need to be toughened.

(Editing by Andrea Ricci)