(REUTERS) - The U.S. Federal Reserve should do all it can to reduce very high unemployment and bring inflation back up to more desirable levels, a top Fed official said on Monday.

It's vital that we keep the monetary policy throttle wide open, John Williams, president of the San Francisco Federal Reserve Bank, told a group of students and professors at Claremont McKenna College.

That will help lower unemployment a little bit quicker, and raise inflation back toward levels consistent with our mandates, he said. And importantly, we want to do so quickly to minimize total economic damage.

Williams, a voting member this year on the Fed's policy-setting panel, has supported recent moves by the U.S. central bank to bolster what he termed on Monday a lackluster recovery.

He joined the majority of his fellow policymakers in last month's decision signaling interest rates will stay near zero through late 2014, a year and a half longer than the Fed had previously projected.

The San Francisco Fed chief is known as a monetary policy dove who is more concerned with the threat of high joblessness than high inflation.

On Monday, he said conditions could merit further policy easing through a third round of quantitative easing, nicknamed

QE3.

In terms of whether we do QE3, this would depend completely on where the U.S. economy is going, he said. If inflation continues to stay very low, and unemployment very high, I think a pretty strong case could be made, based on the logic I gave, to try to boost the economy a little bit more.

With 10-year Treasury yields below 2 percent, there is a limit to how much further the Fed can push down long-term borrowing costs, he said. And even with rates near record lows, a weak housing sector is robbing Fed policy of some of its effectiveness.

If you look at our financial system today, it is still cowering, he said, with lenders so cautious that many homeowners are unable to take advantage of low rates by refinancing their mortgages.

Still, he noted, Japan has pushed long-term rates towards 1 percent, suggesting there is still room for the Fed to do still more.

The Fed has kept interest rates near zero for more than three years, and it has pushed down borrowing costs further by buying $2.3 trillion in long-term securities.

After the Fed last month signaled rates would stay low for nearly three more years, Fed Chairman Ben Bernanke said the central bank stood ready to do still more for the economy, if unemployment remained high and inflation low.

Unemployment in January fell to a three-year low of 8.3 percent, but it is still much higher than the 6 percent to 7 percent rate that most economists believe could be sustained without putting upward pressure on prices and inflation.

Meanwhile, inflation measured by the Fed's preferred gauge fell to 0.7 percent last quarter, well below the 2 percent target the central bank set last month. Williams said he expects inflation to be around 1.5 percent for the next two years.

A recent string of better-than-expected economic data has economists and investors speculating the Fed may hold off from doing more stimulus.

Some Fed officials, including Richmond Fed President Jeffrey Lacker and Philadelphia Fed President Charles Plosser, have suggested the Fed's next move should be to raise rates, possibly as soon as this year.

Williams just last week said he believes the Fed should not raise rates until 2014, and gave no signal that recent data would change his mind.

I'm sticking with my story that economic growth won't be that strong this year, Williams told reporters.

(Editing by Leslie Adler and John Mair)