Republicans' presumed nominee, Sen. John McCain, got the general to repeatedly declare that al Qaeda is a continuing "major threat" — which Mr. McCain says is enough justification alone for a continued U.S. troop presence.

From the Democratic side, Sen. Hillary Rodham Clinton got Gen. Petraeus to acknowledge that U.S. troops were planning to expand their role in the southern part of Iraq because of continued violence, while Sen. Barack Obama said the testimony called for a different standard for success, one that would justify an earlier withdrawal of American troops.

It was a chance for all three to use their committee positions to flex their knowledge of national security issues before a nationally televised audience, just as an uptick in violence in Iraq has put the war back on the front pages.

Mr. McCain sought to defuse repeated charges from the two Democrats that he wants to pursue a 100-year war in Iraq.

"Our goal — my goal — is an Iraq that no longer needs American troops. And I believe we can achieve that goal, perhaps sooner than many imagine," the Arizonan said. "But I also believe that to promise a withdrawal of our forces, regardless of the consequences, would constitute a failure of political and moral leadership."

Mrs. Clinton shot back that she "fundamentally" disagreed with Mr. McCain's belief "that it is irresponsible or demonstrates a lack of leadership to advocate withdrawing troops from Iraq in a responsible and carefully planned withdrawal."

"I think it would be fair to say that it might well be irresponsible to continue the policy that has not produced the results that have been promised time and time again at such tremendous cost to our national security and to the men and women who wear the uniform of the United States military," the New York Democrat said.

Still, in her direct questioning of Gen. Petraeus and U.S. Ambassador to Iraq Ryan C. Crocker, Mrs. Clinton struck a markedly more subdued tone than in the hearing in September, when she told the general that his claims of progress from the surge required the "willing suspension of disbelief."

"I thought it was a very professional approach. I didn't agree with everything she said, but her focus on the issues was not disrespectful," said national security strategist Michael O'Hanlon of the Brookings Institution, who has been critical of the Democrats' troop withdrawal posture and is a supporter of the surge.

Mr. McCain, attempting to appear tougher on the situation in Iraq, began his line of questions by expressing disappointment over the desertion of more than 1,000 Iraqi soldiers and police officers in the recent Iraqi offensive to clean out lawless militias in Sadr City and terrorist attacks on the Green Zone, where U.S. military officials, the American Embassy and other officials are based.

Both Mr. McCain and Mrs. Clinton are part of the Senate Armed Services Committee, which had first crack at the two witnesses. Later in the day, Mr. Obama, a member of the Senate Foreign Affairs Committee, got his chance, and he pointedly returned to the issue of al Qaeda in Iraq that Mr. McCain had raised.

After announcing his early opposition to the war — something that sets him apart from Mrs. Clinton and Mr. McCain, who both voted to give President Bush the authority to invade — he blamed the war for the presence of al Qaeda in the first place.

"They were not there before we went in, but they certainly were there last year, and they continue to have a presence there now," he said, asking Gen. Petraeus whether he anticipated "that there ever comes a time where al Qaeda in Iraq could not reconstitute itself?"

The general replied that "al Qaeda will try to reconstitute just as any movement of that type does try to reconstitute," but the question was whether Iraqi security forces "over time, with much less [U.S.] help, could deal with their efforts to reconstitute."

"That's my point," said Mr. Obama, asking whether Gen. Petraeus believes the Iraqis can be effective in "handling the situation" themselves. The general replied that over time, he believed they could.

Nailing his point down further, Mr. Obama said "I want to be clear. Our goal is not to hunt down every single trace [of al Qaeda]," but to reach a point where "they're not posing a threat to Iraq or using it as a base to launch attacks outside of Iraq. Is that right?"

"That is exactly right," Gen. Petraeus said.