But Mr King said it was "unrealistic" to assume that markets were likely to reopen speedily and it was important that discussions also took place with the UK's major banks about coming up with longer-term solutions.
Mr King's comments to MPs on the Treasury select committee were his first since a meeting with bank chiefs last week.
He pledged to provide the "liquidity assistance" that the system needs to restore confidence, on top of more than £10 billion extra into money markets to ease the clamour for cash among banks.
Mr King said: "I want to assure you that the Bank will provide the liquidity assistance that the system needs in order to restore confidence.
"Such lending can be only a temporary measure but it can be a useful bridge to a longer-term solution."
Mr King said it was too early to say where the discussions with the banks would lead.
However, he said it was important that the risk relating to losses on their lending should remain with the banks' shareholders.
Losses
"The banks neither need nor want the taxpayer to insure them against these losses," he said.
Secondly, a longer-term solution should not be used to subsidise issues of new assets.
Mr King added: "One of the lessons of this financial crisis is that providers of mortgage finance had underestimated the risks, and hence the true cost, of the securitisation process."
Mr King has acted alongside other central banks around the world to improve liquidity, although reports have suggested the Bank is preparing to go further in its cash injections - as well as accepting a wider range of collateral for the funds - following last week's meeting.
The Governor's comments on the credit crunch came as he met MPs to discuss the Bank's quarterly inflation report, which was published last month.
Figures last week showed the official measure of the cost of the living - the Consumer Prices Index (CPI) - reached a nine-month high of 2.5% during February.
The Bank is charged with keeping CPI pegged to 2% and Mr King will be forced to write an open letter to Chancellor Alistair Darling if inflation creeps more than 1% above the target.
The Governor said in February that a letter to the Chancellor this year was "odds-on" as a weaker pound, soaring oil and food costs, and rising household energy bills combine to pile on inflationary pressure before slowing growth brings prices back into check.
Mr King said today that even if commodity prices remained at their present high levels, the Bank's central projection was for inflation to fall back towards the 2% target later this year.
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