Former New York City Mayor Rudy Giuliani speaks at the Ronald Reagan Presidential Library in Simi Valley, California January 30, 2008 where he formally withdrew from the Republican presidential nomination race and endorsed Republican presidential candidate John McCain (R). [Photo: Robert Galbraith/Reuters]

Related: Edwards Quits Bid for White House

               U.S. Republican Presidential Candidates Debate at Reagan Library

U.S. presidential hopefuls Rudy Giuliani and John Edwards said Wednesday they would quit their White House bids, as the so-called "Super Tuesday" when 20 states hold primaries and caucuses draws nearer.

Giuliani, the former New York mayor who had sought to make a leap to the White House, dropped out of the Republican presidential contest officially Wednesday, just hours before he was scheduled to participate with other Republican candidates in a debate at the Ronald Reagan Presidential Library near Los Angeles.

He endorsed Arizona Senator John McCain, a longtime friend and the front-runner in the Republican field.

"I made it clear at different times of this campaign that the one other person that I support for president of the United States was John McCain," he said. "If I endorsed anyone else, you would accuse me of flip-flopping."

Giuliani's endorsement comes as speculation swirls that California Governor Arnold Schwarzenegger, a Republican, will endorse McCain, possibly as early as Thursday.

McCain, appearing with Giuliani at the Reagan Library, thanked the former New York City mayor and called him his friend.

Giuliani said the Arizona senator was the most qualified candidate to lead the country, also referring to him as "an American hero" who shared his vision for the Republican Party.

McCain would be joined at the debate, which would be the Republicans' second in seven days, by former Arkansas Governor Mike Huckabee, Texas congressman Ron Paul and former Massachussets Governor Mitt Romney.

McCain became the front-runner in what had been a wide-open race with Tuesday's victory in the Florida primary.

The nominee is likely to be decided on the coming Tuesday when over 20 states, including California, hold primaries and caucuses -- the biggest one-day round of presidential primary voting in U.S. history.

Meanwhile, Democratic presidential hopeful John Edwards made an announcement to quit his campaign earlier Wednesday at an event in New Orleans, after losing the four states that have held nominating contests so far.

"It's time for me to step aside," he said, adding that he expected a Democrat to win the White House.

A spokesman for Edwards said the former North Carolina Senator would not endorse another candidate at the time of being, but that he might in the future.

Edwards, who brought a focus on poverty and working-class issues to the 2008 Democratic presidential race, stressed his continued commitment to fighting poverty in his New Orleans speech.

"This is the cause of my life and I now have their commitment to engage in this cause," he said before a small group of supporters.

He had announced his candidacy last year in New Orleans, highlighting the city's poverty and its difficulties in recovering from Hurricane Katrina.

With the "Super Tuesday" coming within one week, the Democratic candidates will debate on Thursday at the Kodak Theater in Hollywood.