NEW YORK (CNN/Money) - President Bush endorsed Alan Greenspan for another term as the chairman of the Federal Reserve Tuesday, ending speculation he could punish Greenspan for speaking out against his multibillion-dollar tax cut plan.

The move could also help Bush in his efforts to win re-election in 2004. Keeping a popular central bank chairman, believed by many to be a "maestro" of economic policy, could quiet some of the critics of Bush's handling of the moribund U.S. economy, which has struggled to recover fully from a 2001 recession.

Fed Chairman Alan Greenspan

"Yes, I think Alan Greenspan should get another term," Bush told reporters when asked if the Fed chief has done a "good enough job" to be reappointed. The president made the comments during a roundtable interview with a group of reporters, excerpts of which were released by the White House, Reuters reported.

Bush's comments come on the day Greenspan underwent successful surgery for an enlarged prostate gland.

"He will be recuperating in the hospital overnight and expects to be back in his office later this week," the Fed said in a statement, noting that the procedure was "routine and successful."

Greenspan had a similar operation in June 1994, and the surgery will not interfere with the May 6 meeting of the central bank's policy-setting Federal Open Market Committee, the Fed said earlier.

Greenspan, 77, was first appointed chairman of the nation's central bank by President Reagan in 1987. His current term runs out in June 2004 -- at the height of the presidential election campaign.

He has yet to indicate whether he is interested in serving another term, but various reports have said he enjoys the job and wants to keep it.

After 15 years at the helm of the world's most powerful central bank, Greenspan enjoys legendary status for his role in guiding U.S. monetary policy. Despite criticism for not acting to pop the stock market bubble of the 1990s, he has earned some praise for his handling of the 2001 recession as well as the stock market crash of 1987.

But Greenspan has caused concern in the Bush administration in recent months by saying the economy might not need the tax-cut package the president has proposed. And Greenspan advised caution about the growing federal budget deficit, which could get a great deal larger with Bush's proposals.

Democrats opposed to the Bush plan took heart in Greenspan's remarks, and Sen. Tom Daschle, D-S.D., called them the "kiss of death" for the president's tax-cut package.

President Bush said he would back Federal Reserve Chairman Alan Greenspan for another term. CNNfn's Tim O'Brien reports. Play video (QuickTime, Real or Windows Media)

Some observers even wondered whether Bush would replace Greenspan with a hand-picked candidate when the central bank chairman's term ended next year.

The White House reaction, however, was muted, with press secretary Ari Fleischer saying there was "reasonable disagreement" between the president and Greenspan about the need for economic stimulus.

In the months since, Greenspan and Bush have met a number of times to discuss how the U.S.-led war with Iraq was affecting the economy.

The relatively sanguine relationship between Bush and Greenspan stands in contrast to the relationship between Bush's father and the central bank chairman in the early 1990s.

Supporters of then-President Bush accused Greenspan of acting too slowly to combat a recession in 1990-91, saying the "jobless recovery" that followed cost Bush a bid for re-election in 1992.