By Jeff Mason

COLUMBIA, South Carolina (Reuters) - Race became a focus of the Democratic presidential campaign on Sunday with Hillary Clinton accusing rival Barack Obama of distorting remarks she made last week about the 1960s U.S. civil rights movement.

Obama, who would be the first black president, called this "ludicrous" but said Clinton had offended some Americans who believed her comments last week had marginalized the role of black leader Martin Luther King in advancing those rights.

Clinton, who would become the first woman president, and Obama are locked in a close race for the right to represent the party in the November 4 election to succeed President George W. Bush. Republicans too are in a tight race.

As the Iraq war has moved off the front pages, issues such as the faltering economy have gained attention. Candidates vying for support in states holding nominating contests this month spoke on Sunday of their plans for boosting the economy.

Interviewed on NBC's "Meet the Press," Clinton was asked about remarks to Fox News last Monday, which some had interpreted as giving U.S. President Lyndon Johnson more credit than King for advancing the landmark 1964 Civil Rights Act.

The act outlawed segregation of blacks and whites in schools and other public places. King was a leader of the civil rights movement and won the Nobel Peace Prize in 1964. He was assassinated four years later.

"Dr. King didn't just give speeches. He marched. He organized. He protested," Clinton said on Sunday. "And he campaigned for political leaders including Lyndon Johnson because he wanted someone in the White House who would act on what he had devoted his life to achieving.

"The Obama campaign is deliberately distorting this," said the 60-year-old New York senator, a former first lady.

Obama, 46 and an Illinois senator, has garnered support among blacks, who make up about 13 percent of the population. But Clinton and her husband, former President Bill Clinton, have long had strong support from the black community.

Obama said he had never commented on her earlier statement but said it had "offended some folks who felt that somehow diminished King's role in bringing about the Civil Rights Act.

"She is free to explain that but the notion that somehow this is our doing is ludicrous," he told reporters.

Rival Democrat John Edwards, a former North Carolina senator, took a swipe at Clinton too.

"I must say I was troubled recently to see a suggestion that real change came not through the Rev. Martin Luther King, but through a Washington politician. I fundamentally disagree with that," he told a church group in Sumter, South Carolina.

Democrats are preparing for contests in Nevada on Saturday and South Carolina on January 26 while Republicans are focused on Michigan on Tuesday and South Carolina on Saturday.

ECONOMY TOP CONCERN

Clinton spoke at a church in Columbia, South Carolina, and a member of the predominantly black congregation demonstrated the changing mood of the presidential race, which has seen the sagging economy become voters' top worry.

"The economy to me is the big issue here," said Andrea Gray, 60, saying it was more important than race.

Obama addressed the economy by proposing a $75 billion stimulus plan as he started his campaigning in Nevada. Clinton introduced her own $70 billion stimulus plan on Friday.

Former Massachusetts Gov. Mitt Romney, a Republican, planned to give a speech on the economy on Monday in Michigan, where his father was governor in the 1960s.

Romney has suffered two straight second place finishes in Iowa and New Hampshire. But Romney said on CNN's "Late Edition" that Michigan was not a "do or die" state and he intended to continue the fight through February 5, when 22 states hold nominating contests.

A McClatchy-MSNBC poll showed Romney leading John McCain by 8 points -- 30 percent to 22 percent -- in Michigan with three newspapers in the state endorsing the Arizona senator.

New national polls showed a big McCain jump. A New York Times/CBS News survey showed 33 percent of Republican primary voters backed McCain, followed by Huckabee with 18 percent and Rudy Giuliani with 10 percent. An ABC News/Washington Post poll showed McCain leading with 28 percent, while Huckabee had 20 percent and Romney 19 percent. Both polls found that voters were becoming increasingly concerned about the U.S. economy.

After a rally in Howell, Michigan, on Sunday, McCain criticized Democrats' plans to stimulate the economy. "They want immediate intervention and tax dollars spent. I think that's an option that has to be exercised from time to time, but the last one, not the first one," he said.

Appearing on "Fox News Sunday," former New York Mayor Giuliani denied his campaign was running out of money even though top campaign workers decided to forego their salaries.

(Additional reporting by Andy Sullivan and Jeremy Pelofsky in Michigan, Adam Tanner in Nevada; Writing by Joanne Allen; Editing by Doina Chiacu)

(For more about the U.S. political campaign, visit Reuters "Tales from the Trail: 2008" online at http://blogs.reuters.com/trail08/)