WASHINGTON (CNN) -- Tying to ease conservative unrest over some of his more liberal social positions, former New York City Mayor Rudy Giuliani pledged Monday that as president he would appoint conservative judges to the Federal courts.

"I would do everything that I could to appoint judges that interpreted the Constitution, rather than try to execute their own social policy or social agenda," Giuliani said in a press conference in Washington.

"Your job as a judge is to figure out what the framers meant when they wrote the Constitution, what the people who amended the constitution meant when they amended it, and what the legislators meant when they passed the law, not, in retrospect, what you would like it to mean," he added.

Giuliani's comments come a day after a YouTube video surfaced of a speech Giuliani delivered in 1989, then a New York City Mayoral candidate, in which he said he disagreed with former President Bush's veto of legislation that called for publicly funded abortions.

Louisiana Sen. David Vitter, a conservative Republican, endorsed Giuliani at the press conference, saying he doesn't think the former New York City Mayor will advance a liberal agenda.

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

Watch Giuliani comments on judges