Mr. Wolfowitz, the deputy defense secretary, opened a two-front war of words on Capitol Hill, calling the recent estimate by Gen. Eric K. Shinseki of the Army that several hundred thousand troops would be needed in postwar Iraq, ''wildly off the mark.'' Pentagon officials have put the figure closer to 100,000 troops.

Mr. Wolfowitz then dismissed articles in several newspapers this week asserting that Pentagon budget specialists put the cost of war and reconstruction at $60 billion to $95 billion in this fiscal year. He said it was impossible to predict accurately a war's duration, its destruction and the extent of rebuilding afterward.

''We have no idea what we will need until we get there on the ground,'' Mr. Wolfowitz said at a hearing of the House Budget Committee. ''Every time we get a briefing on the war plan, it immediately goes down six different branches to see what the scenarios look like. If we costed each and every one, the costs would range from $10 billion to $100 billion.''

Mr. Wolfowitz's refusal to be pinned down on the costs of war and peace in Iraq infuriated some committee Democrats, who noted that Defense Secretary Donald H. Rumsfeld and Mitchell E. Daniels Jr., the budget director, had briefed President Bush on just such estimates on Tuesday.

''I think you're deliberately keeping us in the dark,'' said Representative James P. Moran, Democrat of Virginia. ''We're not so naïve as to think that you don't know more than you're revealing.''

Representative Darlene Hooley, an Oregon Democrat, also voiced exasperation with Mr. Wolfowitz: ''I think you can do better than that.''

Mr. Wolfowitz, with Dov S. Zakheim, the Pentagon comptroller, at his side, tried to mollify the Democratic lawmakers, promising to fill them in eventually on the administration's internal cost estimates.

''There will be an appropriate moment,'' he said, when the Pentagon would provide Congress with cost ranges. ''We're not in a position to do that right now.''

At a Pentagon news conference with President Hamid Karzai of Afghanistan, Mr. Rumsfeld echoed his deputy's comments.

Neither Mr. Rumsfeld nor Mr. Wolfowitz mentioned General Shinseki, the Army chief of staff, by name. But both men were clearly irritated at the general's suggestion that a postwar Iraq might require many more forces than the 100,000 American troops and the tens of thousands of allied forces that are also expected to join a reconstruction effort.

''The idea that it would take several hundred thousand U.S. forces I think is far off the mark,'' Mr. Rumsfeld said.

General Shinseki gave his estimate in response to a question at a Senate Armed Services Committee hearing on Tuesday: ''I would say that what's been mobilized to this point -- something on the order of several hundred thousand soldiers -- are probably, you know, a figure that would be required.'' He also said that the regional commander, Gen. Tommy R. Franks, would determine the precise figure.

A spokesman for General Shinseki, Col. Joe Curtin, said today that the general stood by his estimate. ''He was asked a question and he responded with his best military judgment,'' Colonel Curtin said. General Shinseki is a former commander of the peacekeeping operation in Bosnia.

In his testimony, Mr. Wolfowitz ticked off several reasons why he believed a much smaller coalition peacekeeping force than General Shinseki envisioned would be sufficient to police and rebuild postwar Iraq.

He said there was no history of ethnic strife in Iraq, as there was in Bosnia or Kosovo. He said Iraqi civilians would welcome an American-led liberation force that ''stayed as long as necessary but left as soon as possible,'' but would oppose a long-term occupation force. And he said that nations that oppose war with Iraq would likely sign up to help rebuild it.

''I would expect that even countries like France will have a strong interest in assisting Iraq in reconstruction,'' Mr. Wolfowitz said. He added that many Iraqi expatriates would likely return home to help.

In the 1991 Persian Gulf War, many nations agreed in advance of hostilities to help pay for a conflict that eventually cost about $61 billion. Mr. Wolfowitz said that this time around the administration was dealing with ''countries that are quite frightened of their own shadows'' in assembling a coalition to force President Saddam Hussein to disarm.

Enlisting countries to help to pay for this war and its aftermath would take more time, he said. ''I expect we will get a lot of mitigation, but it will be easier after the fact than before the fact,'' Mr. Wolfowitz said.

Mr. Wolfowitz spent much of the hearing knocking down published estimates of the costs of war and rebuilding, saying the upper range of $95 billion was too high, and that the estimates were almost meaningless because of the variables.

Moreover, he said such estimates, and speculation that postwar reconstruction costs could climb even higher, ignored the fact that Iraq is a wealthy country, with annual oil exports worth $15 billion to $20 billion. ''To assume we're going to pay for it all is just wrong,'' he said.

At the Pentagon, Mr. Rumsfeld said the factors influencing cost estimates made even ranges imperfect. Asked whether he would release such ranges to permit a useful public debate on the subject, Mr. Rumsfeld said, ''I've already decided that. It's not useful.''