Europe knows it must do more to persuade financial markets it is coming to grips with its debt problems but there is no question it has the financial firepower to do so, a senior U.S. official said on Friday.

Speaking on condition of anonymity after a day-long meeting of Group of Seven financial chiefs, the U.S. official said there had been a heavy focus throughout the sessions on Europe's debt woes.

The official said Europe was eager to assure markets it could handle the debt problems and said there was no question that they had essentially unlimited capacity to address any funding needs of European banks.

U.S. Treasury Secretary Timothy Geithner later said the G7 -- the United States, Britain, Canada, France, Germany, Italy and Japan -- would do all it could to assist European officials as they work to keep debt problems from spreading to more nations.

European officials fully understand the gravity of the situation there, Geithner said. The G7, alongside the International Monetary Fund, is committed to working with them to decisively address the crisis in Europe.

The U.S. official noted that there had been some discussion about Europe's unhappiness at the IMF saying that Europe's banks might be undercapitalized by as much as 200 billion euros.

The IMF seems to be backing away from that figure, the U.S. official said, adding the European Central Bank has the unquestioned power to ensure funding is available for financial institutions.

The European view is that it is important first to ensure that there is ample financial backing behind European governments to backstop them against debt problems, after which they can deal with questions of bank capital adequacy.

The official claimed there had been broad support for President Barack Obama's announcement on Wednesday night of a $447-billion package to create jobs. It will still require passage of legislation to enact many parts of the U.S. proposal but its promise of job-creating expansion was welcomed.

Geithner commented that the proposals, and the pledge that the U.S. would work to curb its budget deficits over the medium term, was seen as the type of initiative needed to try to ward off a slowdown in growth that affects the global economy.

There was strong support around the table for the plan the president laid out to strengthen growth and restore long-term fiscal sustainability, Geithner said.

(Reporting by Glenn Somerville; editing by Mike Peacock)