WASHINGTON (Reuters) - Republicans blocked the U.S. Senate on Saturday from considering a rebuke to President George W. Bush's Iraq troop buildup, but lawmakers vowed to continue waging a bitter struggle over war policy.

For the second time in two weeks, Republicans senators halted progress on a nonbinding resolution opposing Bush's recent decision to send 21,500 more troops to Iraq. The U.S. House of Representatives passed the resolution the day before.

The Senate's vote in favor of the resolution was 56-34; four short of the number needed to allow the full Senate to debate the measure.

The rare Saturday session came on a day U.S. Secretary of State Condoleezza Rice made an unannounced visit to Baghdad and asserted an U.S.-Iraqi military crackdown was off to a good start.

"The majority in the U.S. Senate just voted against the escalation of the war in Iraq," said Senate Majority Leader Harry Reid (news, bio, voting record), a Nevada Democrat. Seven Republicans, five more than the previous time, had voted for the measure.

"The Senate is not done with this issue," he added. "The Senate will keep trying to force President Bush to change course in Iraq."

But Senate Minority Leader Mitch McConnell (news, bio, voting record), a Kentucky Republican, said the House resolution was a "nonsensical proposition" that asserted support of U.S. troops while disapproving of their mission.

"The Senate was created to block that kind of dealing and today it stops at the doors of this chamber," McConnell said.

Republican senators vowed to block all similar measures unless Democrats promise to also allow consideration of a proposal forbidding a cutoff of funds to U.S. troops.

THE NEXT BATTLE

Both Reid and McConnell mentioned a domestic-security bill coming soon to the Senate floor as a possible venue for their next battle over Iraq.

The 435-member House defied the Republican Bush on Friday, voting 246 to 182 against the troop increase. The measure does not, however, force the president to do anything, and the administration says the president's plan is underway.

The House measure passed with the support of 17 Republicans, many worried about their political fate if they stick with Bush on the unpopular war.

But in the Senate, a minority can block debate, and Democrats have only a 51-49 majority.

Senate Democrats said they would seek ways other than nonbinding resolutions to change Iraq policy, including revisiting the 2002 congressional authorization of the war.

Democrats would "ratchet up the pressure on the president, on those who are still on his side in terms of this policy, until they change," vowed Sen. Charles Schumer (news, bio, voting record), Democrat of New York. "We will be relentless."

McConnell said Republicans would keep trying to shift terms of the debate toward funding, arguing that if Democrats felt the war was wrong, they should vote to cut funds.

House Democrats are considering ways to restrict Bush's use of $93.4 billion in new war funds to keep him from using it for the troop buildup.

South Carolina Republican Sen. Lindsey Graham (news, bio, voting record) said Senate Democrats feared funding votes because it would put numerous presidential candidates on record on the contentious issue.

"If you did have this vote, the radical left would eat every Democratic hopeful for president alive," Graham said.

The White House also looked ahead to the funding battles.

"Both houses of Congress within a matter of weeks will conduct binding votes on a matter of cardinal importance for America's future security and global credibility: whether to fund the president's (spending) request for our military. The president urges both houses to approve his request," a White House statement said.

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