Europe gave a cool reception to a demand from the International Monetary Fund's new head Christine Lagarde to force its banks to bulk up their capital, saying the continent had done enough already.

The European Commission said there was no need to recapitalize the banks over and above what had been agreed after a recent annual stress test check of their ability to withstand economic and financial market headwinds.

I don't think so. This discussion has already taken place between the EU and the IMF, and the IMF is well aware of the results and the follow-up decided after the stress-tests, Commission spokesman Amadeu Altafaj said.

Lagarde, speaking at an annual meeting of central bankers in Jackson Hole, Wyoming, on Saturday urged politicians to act now or risk seeing the fragile recovery derailed.

Banks need urgent recapitalization, Lagarde said. The most efficient solution would be mandatory substantial recapitalization -- seeking private resources first, but using public funds if necessary.

The former French finance minister did not elaborate. The European Union has already urged national governments to provide capital to banks identified as weak by the stress tests if they are unable to raise capital on their own.

Last month a summit of euro zone leaders agreed to let the bloc's 440 billion euro ($632 billion) bailout fund finance the recapitalization of banks if necessary, even in countries which are not receiving international bailouts.

Earlier this month, large French and Italian banks suffered steep share price declines on speculation about their financial strength, prompting France, Italy, Spain and Belgium to impose short-selling bans on financial stocks.

Pressure on European banks to raise more capital had increased in July after European stress tests found eight banks failed to meet capital requirements, revealing a total capital shortfall of 2.5 billion euros ($3.5 billion).

FRESH CAPITAL

However, Lagarde's comments came as stocks in Europe bounced back, tracking a late rally on Wall Street on Friday, after signs that the U.S. Federal Reserve would continue to support the U.S. economy. European bank stocks <.SX7P> were up 1.2 percent on Monday.

Greek bank stocks gained most, with some rallying 20 percent, as they were also boosted by a pending merger of local banks Eurobank and Alpha Bank , raising hopes that Greek banks will be able to sort out their problems without government help.

(Lagarde's) comments won't help to boost confidence in the international financial system, said Gerhard Hofmann, board member of the association of German cooperative banks.

If any European bank needs fresh capital, it would be better to stabilize the institute properly than to discuss it publicly in such a tense market situation, he said.

A source at Spain's economy ministry echoed those comments.

The government has already put in place from the start of this year a recapitalization plan for its financial institutions, with very high requirements, the source said.

Lagarde's statement was one of her first public calls for Europe to take policy action since she became head of the IMF in early July. Previously, the Fund had also urged euro zone leaders to expand the size of the bloc's sovereign bailout fund, an idea rejected by Germany and France.

The IMF's comments matter to Europe, because Brussels is counting on the global lender to help finance a second bailout of Greece, announced by euro zone leaders last month, which envisages 109 billion euros of fresh official funding.

When the first Greek bailout was announced in May last year, the IMF quickly pledged to contribute about a third of the funds, which totaled 110 billion euros.

This time, however, the IMF has not said specifically how much it will provide, and it is unclear if the Fund's emerging economy stakeholders are willing to continue shoveling large amounts of aid into the region.

Brazilian and Indian directors of the IMF have warned against pouring excessive sums of money into Europe.

($1 = 0.696 Euros)

(Additional reporting by Sarah White in London and Lionel Laurent in Paris; Writing by Douwe Miedema; Editing by David Holmes and Susan Fenton)

Germany International Monetary Fund