The Bush administration, confronting a rising casualty toll in Iraq, said Monday that "nothing of value has ever been won without sacrifice."

National security adviser Condoleezza Rice (search) also said a surge of attacks against American forces does not represent a return to major combat operations.

"Major combat operations have not resumed in Iraq (search) by really any stretch of the imagination," Rice said. "What has happened is there are some elements of the old regime that are making common cause with some foreign fighters in what I think could classically be described as an insurgency or insurgency plus terrorism."

Rice sat in the White House briefing room before a bank of television cameras to answer questions from local network affiliates. It was part of the administration's strategy to reach beyond the Washington media -- what President Bush calls "the filter" -- to deliver the White House message across the country.

On a parallel track, Secretary of State Colin Powell (search) told students at City College in New York that "for the sake of civilization, for our security, we must stay the course" in Iraq and also "pay the price."

"There is no question we are being tested," Powell said. But, he said, "we will win -- of that there is absolutely no doubt in my mind."

Returning to the college from which he was graduated in 1958 to mark the 100th anniversary of the birth of Ralph Bunche, an African American who pursued careers in education and diplomacy, Powell said U.S. troops would destroy the terrorists and remnants of the fallen Saddam Hussein government.

As of Monday, 394 U.S. service members have died since the beginning of military operations in Iraq, according to the Pentagon. Some 256 have died since Bush declared on May 1 that major combat operations had ceased.

"He feels acutely every loss," Rice said. "He understands that he is asking the American armed forces and American families to make the great sacrifices.

"But the fact is that nothing of value has ever been won without sacrifice," Rice told NBC affiliate KING in Seattle.

She spoke on the eve of Veterans Day, when Bush is to make a speech honoring the sacrifices of American forces in Iraq and in earlier wars.

Rice said most of the trouble in Iraq has been confined to the so-called "Sunni Triangle" encompassing Baghdad, Fallujah and Tikrit. "Most of this country is stable," she said. "We will get a handle on this security situation and resolve the problem."

Rice said Bush's strategy calls for increasing the number of Iraqis involved in their own security.

"We have nearly 118,000 Iraqis now involved on a daily basis in their own security," Rice told Fox affiliate WAGA in Atlanta. "Much is at stake for the Iraqi people."

She also praised Saudi Arabia for its role in the fight against terrorism. A weekend bombing killed 17 people at a compound housing mostly Arab foreigners in the Saudi capital.

"The Saudis are very serious partners in the war on terrorism," Rice said. "They understand that these terrorists were not just going after the United States and other members of the coalition. They're going right to the heart of the Saudi kingdom, which is why the attack in Riyadh, by the way, killed more Arabs than anything else. This was an attack on the heart of the Saudis, and they understand that."