Mr. Rumsfeld also said for the first time that the attacks against American troops by remnants of Saddam Hussein's security forces, fedayeen fighters and Iraqi prisoners released before the war, were being coordinated at least regionally and possibly nationally.

Mr. Rumsfeld and his top aides had expressed optimism in recent weeks that American troop levels in Iraq could begin to decline as additional allied ground forces arrived later this summer and more newly trained Iraqi police officers took up positions around the country.

But the increasing frequency and sophistication of the attacks against American forces and Iraqis helping them have stirred alarm among American officials and caused commanders and Mr. Rumsfeld to rethink force levels.

"It seems to me that the numbers of U.S. forces are unlikely to go up," he said on the NBC News program "Meet the Press." "Now, could they? You bet. If they're needed, they will be there."

There are 148,000 American and 13,000 non-American troops in Iraq now, with 17,000 more allied soldiers pledged to arrive over the summer. Mr. Rumsfeld said 28,000 of the 60,000 Iraqi police officers needed were now on the job. American occupation leaders also plan to train a new Iraqi army of 12,000 soldiers within one year, expanding it to 40,000 within three years.

As recently as Wednesday, in testimony before the Senate Armed Services Committee, Mr. Rumsfeld had agreed with Gen. Tommy R. Franks, who recently stepped down as the commander of troops in the region, that the overall number of foreign troops in Iraq would stay about where it is for the foreseeable future. At the same time, he suggested that some troops from other nations would replace United States soldiers, reducing the American presence somewhat.

"It would be incorrect to say that we expect that international forces will replace all of U.S. forces," Mr. Rumsfeld said under intense questioning by senators. "We don't anticipate that."

In his testimony, he also said that if the strains of American deployments of ground troops around the world forced the Pentagon to seek to increase the size of the Army and the Marines, "clearly, we will come to Congress and ask for an increase," adding, "But at the moment, we do not see that that's the case."

Mr. Rumsfeld is to be briefed this week by military commanders on how long troops now in Iraq ought to be kept there, and on which units might leave. They would be replaced by other American forces as part of a rotation that changes the mixture of troops from those specialized in intense combat to those better suited for keeping the uneasy peace and sporadic hostilities.

Today, Mr. Rumsfeld confirmed that American officials were bracing for a possible new wave of attacks against United States forces during the next week to coincide with anniversaries tied to Mr. Hussein and the Baath Party.

The anniversaries include July 14, the date of the 1958 coup against the British-backed monarchy, which under Mr. Hussein was celebrated as Iraq's National Day; July 16, the date that Mr. Hussein took power in 1979; and July 17, the date of the Baath Party revolution in 1968.

"We expect that the summer is not going to be a peaceful summer," Mr. Rumsfeld said on the ABC News program "This Week," noting the increased resistance. "It's pretty clear that in a city or an area, there is coordination. We don't have any good evidence that it's nationwide or even a large region, but it's possible."

On "Meet the Press," Mr. Rumsfeld warned of more American casualties, saying: "Are people being shot at? Yes. Is it a difficult situation? You bet. Are more people going to be killed? I'm afraid that's true."

Speaking with more urgency than in the past, Mr. Rumsfeld said capturing or killing Mr. Hussein was paramount so as to deny guerrillas a rallying figure and to ease the fears of other Iraqis that the former president could somehow return to power.

"The fact that Saddam Hussein has not been found does cause a problem," he said on "This Week." "We do need to find him. We do need to get closure."

When asked about the cost of the Iraq mission, Mr. Rumsfeld said on "Meet the Press" that the $2 billion-a-month price tag in April was an estimate by The New York Times. But in fact, the Pentagon comptroller, Dov S. Zakheim, was quoted in The Times on Friday as the source of that figure. Appearing 30 minutes later on "This Week," Mr. Rumsfeld cited the April figure as the Pentagon's and acknowledged that the postwar costs had roughly doubled, to about $4 billion a month.

In discussing the attacks on American forces, Mr. Rumsfeld said on "Meet the Press" that many of them seemed directed at stalling efforts to establish a new Iraqi government and to rebuild the economy.

"The leftovers, the dead-enders from that regime, are targeting our successes," he said. "I'm afraid we are going to have to expect this to go on."