Thursday's bombing in Baghdad's Green Zone that killed at least eight, including three Iraqi parliamentarians, should not distract Americans from the ultimate goal of trying to bring peace to Iraq, Sen. John McCain told FOX News.

"Not always, but for a long time, I'm sorry to tell you, you'll see spectacular suicide bombing attacks because they're the most effective and easiest to do. But they do not overall impact the progress that we can make," the 2008 presidential candidate said.

At a separate event, President Bush also condemned the bombing but said it was evidence that Americans need to continue the fight in Iraq to prevent terrorists from attacking on U.S. soil.

"First of all, I strongly condemn the action. It reminds us, though, that there is an enemy willing to bomb innocent people in a symbol of democracy. In other words, the assembly is a place where people have come to represent the 12 million people who voted, and there's a type of person that will walk in that building and kill innocent life. And that is the same type of person that is willing to come and kill innocent Americans," Bush said after a meeting on the No Child Left Behind reauthorization.

McCain has strongly criticized the Bush administration over its mishandling of the war in Iraq. But the Arizona senator is a staunch supporter of Bush's current strategy to send more troops to Iraq, saying it gives the Iraqi government the best chance to stabilize the government and stop sectarian violence.

McCain on Thursday repeated that the strategy should be given time to work even in the face of seeming setbacks.

"Ask the Israelis how tough it is to stop the suicide bombers. So I can't give you a specific time date, but I do understand the patience of the American people is certainly not unlimited," McCain said.

McCain's push to support the latest troop strategy in Iraq is part of his campaign to boost his popularity following a surprising showing in recent fundraising reports. McCain was widely believed to be the front-runner, but first quarter campaign contributions put him in third place behind chief rivals, former Massachusetts Gov. Mitt Romney and former New York Mayor Rudy Giuliani. Recent preference polls show him trailing Giuliani.

During a trip to a Baghdad market last week, McCain wore a protective vest while speaking optimistically about safety there. Critics including Sen. Barack Obama of Illinois, a Democratic presidential candidate, have pilloried McCain's remarks as overly rosy.

Back in Washington on Thursday, McCain met with Secretary of State Condoleezza Rice to brief her on his latest Iraq trip. The two sought to downplay the impact of the bombing, which Iraqi officials now suggest could be the work of a parliamentarian or staff assistant.

"We've known that there is a security problem in Baghdad, which is why the president has structured a new strategy and why General Petraeus and his commanders are carrying it out. But this is still early in the process, and I don't think anybody expected that there would not be counter efforts by terrorists to undermine the security progress that we're trying to make," Rice said.

McCain said he expects things to get worse before they get better.

"I fully expect the enemy to try to orchestrate more spectacular attacks such as rocketing the Green Zone and other acts which would understandably grab the attention and the headlines in the United States of America because they realize that if they can erode American public's will, then they will be able to achieve success," he said.

McCain also repeated his statement that he is more interested in winning the war than winning a presidential campaign.

"I'm not interested in midterm elections. I'm interested in what the judgment of history will be as to whether we did what was necessary to protect our nation from this force of evil which will now be part of our enemy in Iraq if we fail there, and that's what I'm concerned about," McCain told FOX News.

"I have visited with too many families, too many young men and women who have sacrificed far too much for any of that to enter into a political calculation of mine," he added.

While McCain might be lonely, he's not alone. Also speaking with FOX News, Sen. Joe Lieberman, D-Conn., said he supports McCain's stance on the war.

"I'm with McCain. I think that we are making progress over there with the new general, new troops, new plan. We are at a war, so it's not just all going to be good news from Iraq. But the most significant developments are that in Baghdad, the capital city, the sectarian violence is down as a result of our new program," Lieberman said, just as news of the latest bombing was breaking.

Sen. Lindsey Graham, R-S.C., appearing with McCain outside the White House following a meeting with the president, said the overall impression he got from his trip to Iraq last week with McCain is that the latest strategy is not "too little too late."

"The additional reinforcements when they get in place — and they're all not there yet — will make a substantial difference when it comes to political reconciliation," he said.