He said that the timing and strength of the recovery was "highly uncertain".
Mr King said he saw some reasons for optimism and the pace of economic decline had moderated.
He also said that government plans to stimulate the economy and the weak pound would help.
But he was also cautious and said problems in the banking sector had not yet been fully resolved.
The Bank forecast that inflation should fall to around 0.5% by the end of this year before picking up to around 1.2% in two years' time - below the Bank's target rate of 2%.
Mr King said that said it was too early to ascertain whether the Bank's new policy of quantitative easing was successful but said he had not been disappointed by its effects.
With interest rates as low as they can go, the Bank has been pumping money into the banking system through quantitative easing to stimulate the economy.
The process involves the Bank effectively printing money to buy government and corporate bonds.
"It will take 6-9 months I think before we see more evidence," Mr King said.
Analysts said the inflation report indicated that the Bank's interest rates would likely remain at 0.5% until well into 2010.
"We certainly suspect that while latest data and survey evidence have been markedly improved and even hint that the economy could be close to stabilising, significant relapses remain highly likely," said Howard Archer, economist at Global Insight.
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