Federal Reserve Chairman Ben Bernanke on Tuesday described the Greek debt crisis to lawmakers as a European dilemma but one that could have hit U.S. banks if left unattended, senior senators said.

Chairman Bernanke explained what was going on in Europe, it was basically a European problem but with ramifications probably on a lot of our banks and our banking system if there was no intervention, Senator Richard Shelby, the top Republican on the Senate Banking panel, told reporters after a closed-door briefing Bernanke provided lawmakers.

The Fed chairman met with senators to counter concerns the U.S. central bank's decision to provide dollars to foreign central banks amounts to helping to bail out debt-strapped nations. The action buttressed a European-led $1 trillion plan to stop Greece's debt crisis from spreading.

The Fed used similar currency swap lines to battle the 2007-2008 global financial crisis but closed them in February as markets settled. Some lawmakers criticized that effort to ensure dollar liquidity in overseas markets, saying it put U.S. taxpayer money at potential risk.

Bernanke persuaded most U.S. senators at the meeting on Tuesday that currency swaps are needed to help protect the United States from financial contagion and do not expose it to losses, a senior lawmaker said.

Basically I'm satisfied, I think most of the members were, there, on the chairman's answers that we are well protected, Senate Banking Committee Chairman Christopher Dodd told reporters at the Capitol.

The Fed on Monday posted frequently asked questions about currency swaps on its website, noting dollars the Fed provides would be paid back in full by other central banks, a message repeated by Bernanke on Tuesday.

It seemed to me it is a standard procedure that central banks engage in with each other, Republican Senator Bob Corker said after the briefing.

The politically touchy move by the Fed comes at a difficult time for the central bank. It is already battling efforts on Capitol Hill to remove it from overseeing smaller banks and to open up monetary policy to congressional audits.

The Senate on Tuesday approved an amendment to a wide-ranging financial reform bill that would allow a one-time audit of the Fed's emergency lending during the financial crisis. Initially, the amendment would have allowed repeated audits, but the Fed and its allies in the Senate and Obama administration successfully fought that off.

Fed officials say the currency swaps are necessary to protect the fragile U.S. economic recovery from a serious shock that could result if the Greek fiscal crisis spreads.

Richmond Fed Bank President Jeffrey Lacker forecast little political fallout from the reopening of the swaps programs. The Fed is looking to be more transparent around this round of swaps... We are going to be as transparent as we absolutely can be, he said after a speech in Greensboro, North Carolina.

On Capitol Hill, lawmakers warned that the European turmoil should serve as a wake-up call to the deficit-heavy United States to get its own fiscal house in order.

We could very well end up in the same place without having the courage to do the things that are necessary in this country, Corker said.

The U.S. central bank said on Sunday it was reopening currency swap lines with the European Central Bank, the Bank of Canada, the Bank of England and the Swiss National Bank. On Monday, it reopened a swap line with the Bank of Japan.

In an effort to bolster its case that no taxpayer funds are at risk, the Fed on Tuesday said it plans to make public contractual agreements it has for the reopened swap lines. The Fed will publish details of activity in each of the swaps lines on a weekly basis, the official added.

(With additional reporting by Kristina Cooke in Greensboro, North Carolina and Andy Sullivan and Kevin Drawbaugh, Editing by Chizu Nomiyama)

(Writing by Mark Felsenthal and Tim Ahmann; Editing by Andrew Hay)