BOWLING GREEN, Ohio (Reuters) - Democratic presidential nominee John Kerry said on Sunday he did not anticipate sending more American troops to Iraq and hoped to bring "significant numbers" home during his first term.

Promising a fresh start with U.S. allies alienated by President Bush, Kerry said, "I would consider it an unsuccessful policy if I hadn't brought significant numbers of troops back within the first term. And I will do that."

Kerry made the rounds of the Sunday talk shows with his running mate, Sen. John Edwards of North Carolina, while on a two-week, 3,500-mile trip through battleground states.

He was seeking to capitalize on momentum generated by last week's Democratic convention as a new CNN-USA Today Gallup poll showed he had gained only 1 percentage point over Bush.

The poll of registered voters showed Kerry leading 50 percent to 47 percent for Bush, compared to a larger lead last month, 49 percent to 45 percent.

A Newsweek poll on Saturday gave Kerry a four-point jump, or "bounce," from the convention among registered voters.

The Bush campaign pounced on the Gallup poll to point out that Kerry was the first nominee of either party to receive no bounce from his convention since Democrat George McGovern in 1972. A senior Kerry adviser dismissed the survey as an aberration.

NO EXIT STRATEGY

The four-term U.S. senator from Massachusetts, who voted for the congressional resolution authorizing Bush to use force in Iraq, criticized the president's policy in his speech on Thursday accepting the Democratic nomination.

But Kerry did not offer the exit strategy many Americans are looking for and rejected suggestions his plans were vague.

"No, not at all," Kerry told CBS' "Face the Nation." "The problem is that this administration has lost credibility, they've pushed countries away."

He said on CNN's "Late Edition" he was "not going to go into numbers" of troops he wanted to return home from Iraq by 2008, which would mark the end of his first term if he is elected on Nov. 2.

He tied the withdrawal of American soldiers to his effort to win greater international participation in Iraq, citing increased roles in reconstruction and the decision-making process.

"A fresh start changes the equation, particularly changes it for leaders in other countries who have great difficulty right now associating themselves with our policy and with the United States because of the way this administration has burned those bridges," he said.

RECRUITING ALLIES

Kerry told CBS if the United States showed it had a "smarter, more engaged" foreign policy, "We're going to bring people to our side and we're not only not going to put additional troops there, that's the way to bring our troops home."

In the past, Kerry has not ruled out sending more Americans to join the 140,000 U.S. troops already in Iraq but has said he would encourage other countries, particularly Arab nations, to contribute forces.

Most Arab and Muslim leaders, facing public opposition over pro-U.S. policies, have so far declined to contribute troops to the American-led coalition.

"I don't envision it," he said when asked if he would send more U.S. soldiers. "I believe that my leadership and my plan to approach these countries -- and I'm not negotiating it publicly -- I know what I want to do. I know what I believe can be achieved."

Opinion polls suggest a majority of Americans now believe the decision to invade Iraq last year was a mistake. Kerry and Edwards, who also voted in 2002 to authorize the invasion, have refused to call their votes a mistake.