"The scale of the deficit is truly extraordinary. 12.5% of GDP is not something that anybody would have anticipated even a year or two ago, and this reflects the scale of the global downturn, ," he said.
"But it also reflects the fact that we came into this crisis with fiscal policy itself on a path that wasn't itself sustainable and a correction was needed.
"There will certainly need to be a plan for the lifetime of the next parliament, contingent on the state of the economy, to show how those deficits will be brought down if the economy recovers to reach levels of deficits below those which were shown in the Budget figures."
The BBC's political editor Nick Robinson said the governor tried to play down reports of clashes between himself and the Chancellor Alistair Darling by saying, "I don't think the chancellor is remotely relaxed."
The governor and his colleagues were giving evidence to the committee on the Bank of England's latest inflation report and also on the banking crisis.
Mr King said it was too early to say how long the UK's recovery from recession would take.
What exactly it is that people expect the Bank of England to do?
"There are genuine concerns about how quickly the recovery will pick up. Looking at the clear evidence, [businesses] are finding it hard to access credit from the banking system," he said.
"A combination of that and real uncertainty over the global economy makes it very difficult to be confident of a rapid recovery."
The Bank's Paul Fisher added: "It could take two or three years before banks get really comfortable to lend again."
Separately, the Organisation for Economic Cooperation and Development revised down its forecast for the UK economy in 2009. It now expects output to contract by 4.3%, compared with its previous forecast of a 3.7% fall.
'Reports and speeches'
The governor also re-iterated his call for the Bank of England to be given greater powers, which he voiced publicly last week in his Mansion House speech.
He said that "powers and responsibilities must be aligned" and emphasised that people should understand the limits of the Bank's current powers.
HOW THE SYSTEM WORKS NOW
FSA spots that a bank is failing
Bank of England decides what to do about it
Treasury provides public money and nationalises if necessary
"We were given a statutory responsibility for financial stability in the Banking Act. The question I put to you in February, and to which I've not really received any adequate answer from anywhere, is what exactly it is that people expect the Bank of England to do?" he told the committee.
"All we can do at present, before a bank is deemed by the FSA to have failed, is to write our Financial Stability Report and give speeches.
"If you're content with that, that's fine by me. What you can't do is turn around afterwards and say 'You have the statutory responsibility, why didn't you do something?' when there is nothing we can actually do."
In the UK, oversight of the financial system is carried out jointly by the Treasury, Bank of England and city watchdog, the Financial Services Authority.
Earlier on Wednesday, the Conservatives said that, if elected, they would give the Bank primary responsibility for regulating big banks.
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