Speaking on BBC Radio, Osborne said: "I agree with Christine Lagarde that we need to be alert to the build-up of debt in the housing market. We need to be alert when we see house prices rising.
"I have given the Bank of England tools to do the job, and they should not hesitate to use those tools if they see these developments turning into a risk to the British economy.
The IMF said that rising house prices remained one of the major threats to the recovery alongside poor productivity growth and the the weakness of the banking sector. The withdrawal of low interest rates in the UK and the US could also undermine much of the progress made since the recession should it be misshandled by central banks and treasury policymakers, it said.
The Washington DC-based organisation said: "House price inflation is particularly high in London, and is becoming more widespread. So far, there are few of the typical signs of a credit-led bubble.
"Nonetheless, a steady increase in the size of new mortgages compared with borrower incomes suggests that households are gradually becoming more vulnerable to income and interest rate shocks," it added.
Lagarde also questioned the Help to Buy scheme, which has subsidised mortgage deposits, mostly for first-time buyers.
She recognised that the programme allowed "creditworthy lower-income households to purchase homes, especially outside London and the south-east" and it unlocked cheaper credit for lower income borrowers.
However, she warned that a "significant increase" in take up should sound alarm bells and "the Treasury may wish to consider whether it should be modified or even remains necessary for the full three years of the policy. And as the volume of high loan-to-value transactions rises, the financial policy committee will need to evaluate if the programme is contributing to financial risks".
The financial policy committee, an arm of the Bank of England, has already urged regulators to be vigilant about homebuyers stretching their finances to purchase a property.
Treasury officials are understood to be confident that restrictions on home loans will cool the market over the coming months without the need for a hike in interest rates. New figures from Nationwide showed a slowing of price rises at 0.7%, lower than the 1.2% recorded in April. Also the building society's three-month growth figure, which gives a less volatile picture of the market than month-on-month comparisons, also fell, from 2.5% in April to 2.3% in May. That brought it to the lowest level since August 2013.
The IMF has voiced concern in the past over the UK's path out of recession. Earlier this year, its chief economist, Olivier Blanchard, said that while growth had rebounded more strongly than anticipated on easier credit conditions and increased confidence, "the recovery has been unbalanced, with business investment and exports still disappointing".
The booming housing market has concerned most economists. Prices have rocketed in London and the south-east while hotspots around the country have also recorded strong house price rises.
Earlier this week, Nationwide reported a 13th consecutive month of house price rises, sending the cost of an average UK home to £186,512 – more than the previous peak reached in October 2007 before the financial crisis took hold and the overall housing market started to go into freefall.
The latest IMF report said it expected the recovery to continue over the next few years, though not at the current rate of more than 3%.
The IMF report said: "Good macroeconomic performance is expected to persist. Real GDP growth is projected to remain strong this year, before gradually returning to trend rates, driven by further rebalancing toward business investment and a gradual recovery in productivity. Inflation is expected to revert to target."
The IMF urged the Bank of England to maintain low interest rates to maintain the recovery, a stance that will dismay many economists in the City who want an immediate hike to cool the housing market.
"Monetary policy should stay accommodative – for now. With inflation below target, contained cost pressures, and excess supply, monetary policy should remain on hold."
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