WASHINGTON (CNN) -- Last week's bombing in the cafeteria where Iraqi lawmakers eat demonstrates the failure of President Bush's latest strategy for the war, Democratic presidential candidate John Edwards said Monday.

"It's absolutely clear that the surge is, in fact, failing. The attack on the Iraqi parliament inside the Green Zone is clear evidence of that," Edwards told CNN's "American Morning."

The suicide bomber killed one lawmaker and wounded 22 people, 14 of them lawmakers, Iraqi officials said.

Like the rest of the Democratic field of U.S. presidential contenders, Edwards is an outspoken critic of the war. He told CNN if he were president now, "I'd start taking troops out of Iraq. I would make it clear to the government that we're redeploying out of Iraq over the course of the next year or so."

He said he would engage with all the other countries in the region, including Iran and Syria.

While Edwards trails Sens. Hillary Clinton and Barack Obama in national polls and fundraising, he told CNN he is undeterred.

His strategy, he said: "I win in the early states. I mean, it's the way the nomination is always decided." Those "early states" are the ones holding their nominating contests first.

"I'm ahead in Iowa, strong in Nevada, doing well in New Hampshire," Edwards said, adding that his home state of South Carolina -- where he has a strong advantage -- will be fourth.