NEW YORK (AFP) - The dollar fell against the euro Friday as investors welcomed Germany's signal of willingness to rescue Greece as it edges toward defaulting on its debt. The market staged a strong relief rally after German Chancellor Angela Merkel tempered her terms for a new Greek debt rescue. Dealers said the euro and European stock markets turned around sharply higher as Merkel changed tack, agreeing that private investors would take part on a voluntary basis rather than be forced to stump up new cash for Athens. The euro traded at $1.4301 around 2100 GMT, up from $1.4209 a day ago. The dollar also fell against the Japanese currency, to 80.03 yen from 80.67. "Signs that Germany is finally willing to back down on their calls for significant burden sharing by Greek bondholders has instilled hope that reconciliation between German Chancellor Merkel and French President Sarkozy is the first step to a rescue plan for Greece," said Kathy Lien at GFT. Merkel and Sarkozy both stressed after a Berlin meeting that an agreement was needed quickly, with a European Union summit due next week, and that the Greek debt problem had to be resolved. Their remarks gave nervous investors a much-needed boost after weeks of growing speculation that Athens was near default. "There are still risks out there -- Greece still needs to get its next tranche of bailout funds and political risk abounds -- but for now the euro is rallying on the back of increased optimism the Greek crisis won't spread to Portugal, Ireland or Spain," said Kathleen Brooks, research director. In late New York trade, the dollar fetched 0.8486 Swiss franc, compared to 0.8482 Thursday. The pound firmed to $1.6186 from $1.6157.