An unidentified war protester yells during a speech by Republican presidential candidate Sen. John McCain, R-Ariz., to the National Association of Latino Elected Officials meeting Saturday in Washington.

Washington ? Presidential rivals John McCain and Barack Obama on Saturday vied for the support of Hispanics, beginning a four-month courtship of a pivotal voting constituency by vowing to revamp immigration policy.

“I come from a border state, my dear friends. I know these issues,” McCain told Hispanic elected officials. The Republican senator from Arizona said overhauling the country’s broken immigration system, not just securing its borders, “will be my top priority.”

Appearing later before the same audience, Obama accused McCain of walking away from comprehensive immigration reform. The Democratic senator from Illinois said: “We must assert our values and reconcile our principles as a nation of immigrants and a nation of laws. That is a priority I will pursue from my very first day.”

The two spoke separately to some 700 Hispanics attending the National Association of Latino Elected and Appointed Officials conference. It’s the first of three such appearances each is scheduled to make to Hispanic organizations in less than a month, underscoring the importance of the nation’s fastest-growing minority group.

Both McCain and Obama were warmly received at NALEO; the crowd gave each standing ovations and cheered loudly. When McCain spoke, the audience shouted down anti-war protesters who interrupted the Republican’s speech four times. The audience chanted Obama’s name when the Democrat entered later. As he took the stage, Obama said “Si, se puede!” – his “yes we can” campaign slogan in Spanish – and the crowd echoed him.

Earlier, McCain met separately and privately with Iraqi President Jalal Talabani and Philippines President Gloria Macapagal-Arroyo, while Obama stopped by Walter Reed Army Medical Center to visit wounded war veterans. McCain also attended an evening fundraiser in Kentucky, where he criticized anew Obama’s withdrawal from the public financing system and said, “Senator Obama’s word cannot be trusted.”

Hispanics, however, were the primary focus as each makes an aggressive play for this up-for-grabs group that’s likely to carry weight in battleground states of Nevada, Colorado, New Mexico and others with large numbers of Spanish-speaking voters.

A recent AP-Yahoo News poll showed that Obama lead McCain among Hispanics, 47 percent to 22 percent with 26 percent undecided.

Still, Obama, who is trying to become the first black president, doesn’t have a lock on this volatile group. During the Democratic primary, Hispanics referred rival Hillary Rodham Clinton to Obama by nearly 2-to-1.

McCain, for his part, senses opportunity and is hoping to build on Republicans’ recent inroads in this Democratic-trending group.

President Bush captured about 40 percent of the Hispanic vote in 2004, the most ever for a GOP presidential candidate. His Democratic rival John Kerry won 53 percent, down from the 62 percent former Vice President Al Gore got in 2000.

This year, immigration reform, a touchstone issue for Hispanics, is a wild card.

Both McCain and Obama support an eventual path to citizenship for millions of immigrants in the country illegally, and, thus, the issue isn’t expected to be a major point of differentiation in the campaign. Still, Hispanics will be paying careful attention to what is said on the subject.

McCain co-sponsored broad bipartisan Senate legislation last year that would have overhauled the immigration system and improved border security; the legislation split the GOP and critics pushed for a border-enforcement only approach. After the measure failed, and in the heat of the Republican nomination race, McCain emphasized the need to secure the borders first before enacting other reforms, which he said were still needed.