UPDATE 1-Norway's banks need more financial muscle-regulator

* Use of covered bond may need to be curtailed: regulator

* Banks may underestimate property market risks: regulator (Adds detail)

OSLO Oct 16 (Reuters) - Norway's banks need to strengthen their financial position further to withstand external shocks and should reduce their reliance on mortgage-backed bonds, the country's banking regulator said on Tuesday.

Mortgage-backed, or so-called covered bonds, are a cheap source of funding, but have become so popular as to pose a potential risk to the financial system if house prices fall, the Financial Supervisory Authority of Norway said in a report.

In the good times, covered bonds may crowd out other forms of funding while in bad times, this source of funding could dry up quickly, the regulator said.

"In downturns accompanied by falling house prices, this funding source may rapidly dry up at the same time as other funding opportunities are weakened because the best loans have been mortgaged," it said. "Hence covered bonds may add a detrimental, procyclical element to banks' funding and lending."

Although the regulator said "consideration" should be given to curtailing the use of covered bonds, it did not propose any specific measures and said a change cannot undermine the established covered bond market.

It added that while Norway's banks are profitable and well capitalised, they need to further strengthen their financial position and should diversify their funding.

It also highlighted the risk from the mortgage market, especially after a period of rapid property price rises.

"There is a danger that banks individually underestimate the systemic risk associated with such expansion," it said.

"Continued strong growth in house prices and household debt could well be followed by a significant setback which will impact on a broad front and produce substantial knock-on effects in the economy." (Reporting by Balazs Koranyi and Terje Solsvik; Editing by Mark Potter)