William Dudley, the president of the Federal Reserve Bank of New York and a voting member of the Federal Open Market Committee, said in a speech in New York that he believes “further action is likely to be warranted” unless economic activity promptly picks up.

Dudley said the current rates of unemployment, at 9.6%, and inflation, at 1.5%, are “unacceptable.” He said the Fed must take action to prevent overindebted households from taking another hit and further slowing the economy.

“To ensure that the more favorable trends in household balance sheets continue, the economic environment needs to become more supportive,” Dudley said.

The remarks were taken as the latest sign that the Fed is moving toward another round of so-called quantitative easing, in which the central bank buys Treasury securities from banks to push down long-term interest rates.

Doing so would tend to weaken the dollar by suppressing the interest rates investors can expect to earn on assets here. The dollar tumbled again, with the trade-weighted dollar index falling to its lowest level since January. The dollar fell to $1.37 to the euro and was under 84 yen.

The remarks also marked a response to comments in recent weeks by some skeptics within the Fed of the merits of QE.

Dudley was particularly blunt on the subject of inflation, warning that declining inflation expectations meant the Fed “must be clear and resolute in its commitment to its price stability objective.”

The Fed fingered low inflation as a threat to recovery for the first time in its statement last month. The worry is that falling inflation could retard growth by raising the real cost of borrowing.

“As long as inflation remains muted, QE2 remains an inevitability,” said CMC Markets strategist Ashraf Laidi.

At the same time, the Fed’s statement Sept. 21 was somewhat inconsistent, claiming at once that inflation readings were too low but that inflation expectations were stable.

Dudley made clear Friday that, unlike some other people on the 10-member Fed policy board, he isn’t ambivalent on the issue.

Currently, my assessment is that both the current levels of unemployment and inflation and the timeframe over which they are likely to return to levels consistent with our mandate are unacceptable. In addition, the longer this situation prevails and the U.S. economy is stuck with the current level of slack and disinflationary pressure, the greater the likelihood that a further shock could push us still further from our dual mandate objectives and closer to outright deflation.

Though another round of Fed action has many critics, proponents believe the Fed can shelter a weak economy from another shock by keeping rates low, giving household balance sheets more time to recover from the meltdown of 2008.

Even in today’s challenging circumstances, lower long-term rates would support the economy through a number of channels. Lower long-term rates would support the value of assets, including houses and equities and household net worth. Lower long-term rates would make housing more affordable and support consumption by enabling households to refinance their mortgages at lower rates. This would increase the amount of income left over for other spending.

So households may get more dollars. The big question now is what they will be worth.