Government stress tests of how 19 major banks would endure a sharp downturn in the economy already appear to be helping banks gain access to private capital, a key element in economic recovery, Federal Reserve Chairman Ben Bernanke said on Monday.

Bernanke also assured a conference here that the dollar would be strong, because the U.S. central bank would keep inflation at bay by raising interest rates when the time is right.

But his talk on Jekyll Island, where top Wall Street bankers conceived of the modern U.S. central bank at a secretive meeting nearly 100 years ago, focused on last week's crucial assessment of the health of the big U.S. banks.

The initial indications are encouraging, Bernanke told a conference organized by the Atlanta Fed.

Many of the banks are well ahead in finding private-sector options for increasing their common equity, and several have announced plans for new equity issues, he said.

Another positive sign in the aftermath of the tests is that several banks have announced plans to issue long-term debt not guaranteed by the Federal Deposit Insurance Corp, Bernanke said.

Even so, the Fed chairman cautioned it will be some time before it is possible to say whether the exams, which put banks' portfolios through bleaker-than-expected scenarios for economic output, unemployment and house price declines, will fully restore investor confidence and assure banks' access to private capital.

The Fed and other regulators announced last week that 10 of the 19 firms tested would need to raise an additional $74.6 billion to be adequately buffered against the worst-case economic scenario.

We hope that in two or three years we will be able to reflect on the banking system's return to health with a sharply diminished reliance on government capital, he said.

Turning to the U.S. economy during a question and answer session after the speech, Bernanke said the Fed would ensure the strength of the dollar by making sure that inflation did not take hold.

I think the issue at hand is whether or not the dollar will retain its value, and I think it will. I think the dollar will be strong. I think it will be strong because the U.S. economy is strong. And it will also be strong because the Federal Reserve is committed to assuring that we have price stability, he said.

The Fed has cut interest rates to almost zero and pumped hundreds of billions of dollars into financial markets to keep them from freezing in panic over bank losses.

The dollar had strengthened somewhat in the latter part of last year as investors sought its security as a safe haven.

But as the Fed cut rates and pumped up the supply of credit, alongside projections for massive U.S. budget deficits, there have been concerns the currency might weaken.

We are currently, of course, being very aggressive because we are trying to avoid another form of price instability, which is deflation and weakening prices and economic growth.

But we are also committed to removing accommodation in a timely way to ensure that as we come out of this episode and we move back to sustainable recovery, we will have price stability, Bernanke said.

Fed policy-makers are also focused on ensuring that they can pull back the central bank's unprecedented infusions of cash into the economy to prevent unwanted inflation from taking hold when the economy begins to strengthen, he said.

A majority of the members who made these projections just recently took 2 percent as being an appropriate number for inflation, he said. Somewhere between 1-1/2 to 2 percent is basically the number that our committee has individually stated is the appropriate medium-term inflation rate.

To achieve that we need to demonstrate that we will be able to exit from the balance sheet position that we currently have, and have been working on this intensively, he said.

(Editing by Leslie Adler)