Story Highlights• Sens. Obama, Clinton battle for support of black voters at civil rights event
• Clinton: Voting Rights Act is giving me a chance to live my dreams
• Obama: "Don't tell me I don't have a claim on Selma, Alabama"
• Bill Clinton receives voting rights museum award
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SELMA, Alabama (CNN) -- The top two Democratic presidential contenders fought Sunday for the support of African-American voters in a place infamous for a bloody clash between voting rights protesters and police.
Sens. Hillary Clinton and Barack Obama spoke at events marking the 42nd anniversary of the 1965 Selma voting rights march, a turning point in the civil rights movement that led to the passage of the Voting Rights Act.
On that day, police, enforcing Gov. George Wallace's ban on demonstrations, attacked more than 500 protesters with tear gas and batons as they marched from Selma to Montgomery.
After their speeches, Obama and Clinton greeted each other at a rally re-enacting part of the march across the Edmund Pettus Bridge. (Watch Sens. Clinton and Obama declare themselves the product of Selma )
Democratic Rep. John Lewis, one of the leaders of the Selma march and now a Georgia congressman, said the competition between the senators for black voters is "a very difficult position to be in, but it's a good position to be in."
"We have choices," Lewis said.
Speaking separately at two traditionally African-American churches, Clinton and Obama portrayed themselves as beneficiaries of sacrifices made at the bloody march. (Watch each candidate offer a message about civil rights )
Obama, of Illinois, said his racial ties to the event began when his African father met his mother, a white woman from Kansas.
"They looked at each other and they decided, 'We know that, in the world as it has been, it might not be possible for us to get together and have a child, but something is stirring across the country because of what happened in Selma, Alabama, because some folks are willing to march across the bridge. And so they got together, and Barack Obama Jr. was born.
"So don't tell me I don't have a claim on Selma, Alabama," Obama said. (Watch Obama explain how his racial experience ties him to Selma )
Clinton: 'I'm grateful to all of you'
In her remarks, Clinton mentioned her rival presidential candidate, Obama.
"The Voting Rights Act gave more Americans from every corner of our nation the chance to live out their dreams. And it is the gift that keeps on giving," Clinton said. "Today it is giving Sen. Obama the chance to run for president of the United States. And by its logic and spirit, it is giving the same chance to Gov. Bill Richardson, a Hispanic, and, yes, it is giving me that chance, too." (Watch Sen. Clinton say, "we will never forget the blows that they took" )
The New York senator added, "I know where my chance came from, and I am grateful to all of you who gave it to me."
Clinton also mentioned her husband, former President Bill Clinton, who accompanied her to Selma and was inducted into the Voting Rights Hall of Fame. (Watch how the former president can help Sen. Clinton )
Obama attacks poverty, inequality
Obama did not mention Sen. Clinton in his remarks at Brown Chapel A.M.E. And as he tackled a litany of issues such as health care insurance, victims of Hurricane Katrina and racial equality, he did not mention the Iraq war.
"We've got too many children in poverty in this country," Obama said," and everybody should be ashamed."
Obama also mentioned, "the disparity in terms of how people are treated in this country continues. It has gotten better, and we should never deny that it's gotten better, but we shouldn't forget that better is not good enough, that until we've got absolute equality in this country in terms off people being treated on the basis of their color or their gender that that is something that we've got to continue to work on."
Obama: My ancestors owned slaves
Obama also told listeners Sunday that his ancestors on his mother's side included a slave-owner, an acknowledgement that confirmed a recent media report. He called it part of the United States' "tortured, tangled history."
The Baltimore Sun reported Friday that "forebears of his white mother owned slaves, according to genealogical research and census records."
The appearances by Sens. Obama and Clinton came about a week after their campaigns tussled over public criticism against Clinton by Obama supporter and Hollywood movie mogul David Geffen. In an interview with New York Times columnist Maureen Dowd, Geffen called her "incredibly polarizing" and said Republicans believe "she's the easiest to defeat.'' (Read more about the Hollywood dust-up)
In addition, Geffen, once a close ally of the Clintons, was quoted in the column describing Bill Clinton as a " 'reckless guy' who 'gave his enemies a lot of ammunition to hurt him and to distract the country.' "
Clinton 'has a very strong card'
But despite Geffen's reported opinions, a political strategist says Sen. Clinton's association with her husband is a powerful tool in the fight for African-American support.
"There is no white politician in America who is more popular in the African-American community than Bill Clinton," said Jamal Simmons, a Democratic strategist. "So she has a very strong card to play."
The results of one recent poll suggest that card is one she may need. An ABC News-Washington Post survey, taken last month, found that Obama was the choice of 44 percent of black Democrats, compared to 33 percent for Sen. Clinton, with a sampling error of plus or minus 8 percentage points. That was a marked shift from the beginning of the year, when she led Obama 60 percent to 20 percent. (Full story)
However, the poll found that the New York senator's favorable rating among black voters was 85 percent, compared to 70 percent for Obama, although his favorability has climbed 16 points since the beginning of the year.
Simmons said that while black voters have a great deal of loyalty to Bill Clinton, "the question is whether that loyalty transfers to Hillary Clinton, and that's really the test she'll have to meet."
CNN's Trisha Henry and Mary Snow contributed to this report.
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