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Republican presidential hopeful Rudy Giuliani picked up an endorsement Monday from Sen. David Vitter of Louisiana, who said he's backing the former New York City mayor even though he disagrees with his stances on social issues.

"Rudy has the strong unwavering leadership and sound judgment that we so clearly need in this time of war and terrorist threats," Vitter said at a news conference with Giuliani.

The ex-mayor is sitting atop national polls for the GOP nomination, and is trying to maintain his lead by convincing Republican voters that they should support him even though he is pro-choice, pro-gun control and pro-gay rights.

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To allay concerns, the former New York City mayor has emphasized that he would appoint federal judges who "strictly interpret" the constitution, another pet issue of conservatives.

Vitter's endorsement was meant to validate Giuliani's case.

"Obviously, I disagree with Rudy on some significant social issues, and these are very important to me and to many of the people I represent," Vitter said. However, he said, after numerous meetings with Giuliani, "it's very clear to me that he's not running for president to advance any liberal social agenda."

Vitter said any concerns of his were alleviated by Giuliani's stance on judges.