European banks are facing a reckoning over hundreds of billions of dollars in loans extended to the continent’s cash-strapped governments with potential losses so large, if countries default, that some financial firms could be put out of business.

The tumbling value of government bonds issued by some European governments is already undermining the health of major banks. On Wednesday, Moody’s Investors Service cut the credit rating of two large French banks, due to their holdings of Greek government bonds and to wider concerns about whether investors will continue to trust European banks with their money.

On Thursday, the European Central Bank announced that it would provide European banks loans in dollars to help shore up investor confidence. The ECB said it would coordinate with the Federal Reserve, Bank of England, Bank of Japan and the Swiss National Bank to offer three medium-term loans through 2011.

If a major bank were to fail, that could send shock waves across the Atlantic, buffeting U.S. financial companies with close ties to their European counterparts or major investments in Europe.

The downgrades by Moody’s added fuel to a debate among European and U.S. policymakers over whether the continent’s banks are mostly healthy or instead need billions of dollars in additional capital to withstand likely losses on loans made to countries such as Greece, Portugal and Italy.

Greek bonds are already being resold at half their face value because of the high risk of default. If these losses mount, they could eat away at the capital buffer of banks across Europe, raising the prospect of an outright bank failure — which some financial analysts fear could cause the global financial system to seize up as it did after the Wall Street investment bank Lehman Brothers collapsed in 2008.

Capital point of contention

The question of whether European banks are dangerously short of capital will be a point of contention as European finance ministers gather in Poland on Friday and the International Monetary Fund holds its annual meetings next week. IMF Managing Director Christine Lagarde has argued that European banks need a quick and large capital infusion, and U.S. Treasury Secretary Timothy F. Geithner in a CNBC interview on Wednesday said that European leaders are “behind the curve” in addressing the region’s banking and other problems.

In cutting the rating of Credit Agricole, Moody’s cited the French firm’s “sizeable exposure to the Greek economy.” The rating company downgraded Societe Generale because of broader concerns about the outlook for French banks. This action may make it more difficult or more expensive for the banks to raise the money they need to operate — bad news in an environment where financial firms already mistrust each other and are charging more to lend to each other.

French bank officials have said they regard their capital buffers as adequate, and French central bank governor Christian Noyer on Wednesday said Moody’s action was “relatively good news.” With some investors predicting that Moody’s would slash the banks’ rating even more, Noyer told French radio, “It’s a very limited downgrade,” according to wire service reports.

Some banks have been turning to the European Central Bank for help. On Wednesday, the ECB reported that two European banks had tapped it for dollar-based loans, a sign the firms were struggling to find the money they need on the open market. The banks were not named.

In an interview Tuesday, Lagarde said that possible losses on government bonds, combined with the slowdown in the European economy, may make banks overly cautious, restricting lending at a time when more credit is needed to boost economic activity.

“Banks have to be in a position to make loans,” she said. “The risk is that they take the view that deleveraging is the way to go. . . . We see that as a major threat to growth.”

European regulators examined the strength of European banks in July, and these “stress tests” yielded new information about which firms have lent the most money and made the biggest investments in the region’s weakest economies.

The sums involved are substantial, potentially dwarfing the amounts of capital banks have set aside as a buffer against possible losses. According to data from the Bank for International Settlements, European banks as of April 1 had more than $2.1 trillion at risk in Greece, Ireland, Portugal, Spain and Italy, nations that are struggling with high public debt, low growth and waning investor confidence. Greece, Ireland and Portugal have already received international bailouts. Spain and Italy are battling to avoid the need for help.

French and German banks alone hold about $260 billion in government bonds from those five countries, the BIS data show.

Financial analysts and the banks themselves increasingly recognize that these holdings may be worth less than their face value. But estimating the possible losses — and deciding whether banks should account for them now — could prove controversial. These steps could force Europe to declare that nations such as Italy or Spain are poor credit risks.

Since the advent of the 17-nation currency union a decade ago, European banks have been encouraged to buy government bonds under rules that have treated them as risk-free investments that would almost certainly be repaid.

That approach has proved faulty. In their most recent financial statements, some European banks have admitted as much by “writing down” the Greek bonds on their books — in other words, acknowledging they are worth less than previously stated.

The question remains open of whether the bonds of other countries should receive similar treatment. The answer depends in part on what happens in Greece. If a Greek default is avoided or limited in scope, with losses to bondholders kept to a minimum, then bonds issued by large nations like Italy and Spain won’t have to be written down.

But if Greece were to default altogether, it would raise the risk of the same happening elsewhere and force banks to prepare for potentially devastating losses on bonds of other governments.

In its analysis, Moody’s assumed banks might have to write off as much as 60 percent of the value of their Greek bonds, 50 percent of their Irish and Portuguese bonds, 10 percent of their Spanish bonds, and 7 percent of their Italian bonds.

Hung Tran, deputy director of the Institute of International Finance, said the likely losses on government bonds were “manageable” for banks in Europe. But he also said Europe must acknowledge that different countries pose different credit risks.