Republican Rudy Giuliani and Democrat John Edwards abandoned their failing U.S. presidential bids on Wednesday, narrowing the race to two main candidates on each side before next week's nomination voting in more than 20 states.

Giuliani, the one-time front-runner who finished a distant third in Florida's Republican primary on Tuesday, travelled to California to endorse Arizona Sen. John McCain in a Republican battle against former Massachusetts Gov. Mitt Romney.

"Today I am officially announcing my withdrawal as a candidate for president of the United States," Giuliani said at the Ronald Reagan presidential library in Simi Valley before a televised Republican presidential debate.

"John McCain is the most qualified candidate to be the next commander in chief of the United States."

McCain, standing beside his longtime friend, said all Americans recalled the former New York mayor's leadership after the September 11 attacks in 2001 and he predicted Giuliani would be his "strong right arm" in the campaign.

California Gov. Arnold Schwarzenegger will endorse McCain on Thursday in Los Angeles, campaign aides said.

The backing of the moderate Republican governor could be an important boost for McCain in California, adding to his momentum before the heavyweight state holds its crucial primary as part of next week's coast-to-coast voting.

The candidates are in the early stages of a state-by-state battle to pick Republican and Democratic presidential nominees. The winners from the two parties will face off in the November 4 election to succeed President George W. Bush.

HISTORIC DEMOCRATIC RACE

The withdrawal of Edwards means Democrats will field a history-making ticket.

Regardless of whether Illinois Sen. Barack Obama or former first lady Hillary Clinton wins the nomination, it will be the first time a black or a woman has headed a major U.S. party's presidential slate.

Edwards, a former North Carolina senator, travelled to New Orleans, where he launched his campaign more than a year ago, to make the surprise announcement he was pulling out.

He had vowed last week to stay in the race until Tuesday, when almost half the U.S. states vote to pick candidates for the November election.

"It is time for me to step aside so that history can blaze its path," said Edwards, who campaigned as the champion of low- and middle-income families.

Edwards did not immediately endorse either of his rivals.

Giuliani's withdrawal leaves McCain facing a strong challenge from Romney.

At the debate in California, Romney and McCain accused each other of pursuing liberal policies out of step with mainstream Republicans.

Former Arkansas Gov. Mike Huckabee is still formally in the Republican race but his lack of campaign money and limited appeal beyond Christian conservatives has left him trailing.

"This isn't a two-man race," Huckabee, a Baptist preacher, said at the debate as McCain and Romney challenged each other's claims to the conservative high ground. "You want to talk conservative credentials, let me get in on that."

In the liveliest exchange of the debate, Romney accused McCain of "dirty tricks" for what he said was misrepresentation of his views on the Iraq war. McCain said Romney's negative "attack ads" had set the tone for the campaign.

Giuliani did little campaigning in the early voting states, focusing his efforts on a strong showing in Florida, the fourth most-populous state with a large number of retirees from the Northeast. But he finished a disappointing third, barely above Huckabee.

Admitting to some bitterness, Giuliani said that was tempered by satisfaction at endorsing McCain, whom he called "a man of honour and integrity" who could be trusted in a crisis.

McCain and Romney split the previous four Republican nominating contests. McCain won in South Carolina and New Hampshire and Romney carried Michigan and Nevada, the latter a state scarcely contested by other Republicans.

Huckabee won the opening contest in Iowa.