MILWAUKEE (Reuters) - Democratic presidential candidates Hillary Clinton and Bernie Sanders clashed sharply in a debate on Thursday over their support for President Barack Obama, with Sanders accusing Clinton of “a low blow” after she compared him to Republicans.

As the Democratic race moves to states with large minority populations, both candidates openly courted black and Hispanic votes during a debate that was far more restrained and cordial than last week’s contentious debate in New Hampshire.

In the sharpest exchange of the night, Clinton attacked Sanders for being too critical of Obama, who is extremely popular with the black voters who will play a big role in the outcome in South Carolina and other upcoming nominating contests.

“The kind of criticism that we’ve heard from Senator Sanders about our president, I expect from Republicans, I do not expect from someone running for the Democratic nomination to succeed President Obama,” said Clinton, who served as secretary of state during Obama’s first term.

“Madam Secretary, that is a low blow,” said Sanders, a U.S. senator from Vermont. Sanders said he had been an Obama ally in the Senate even if he did not always agree with him.

“Do senators have the right to disagree with the president?” Sanders said.

Clinton, who has eagerly embraced Obama’s legacy, said Sanders had called Obama weak and a disappointment, and “that goes further than saying we have our disagreements.”

With Clinton looking to rebound after her crushing 22-point loss to Sanders in the New Hampshire primary on Tuesday, the two also differed over healthcare and Wall Street.

Even so, the restrained exchange on Thursday was unlikely to change the trajectory of a race that has intensified dramatically over two weeks.

Slideshow ( 15 images )

Clinton accused Sanders of misleading Americans on his healthcare. She said his proposal for a single-payer, Medicare-for-all healthcare plan would mean dismantling the program known as Obamacare and triggering another intense political struggle.

“Based on every analysis I can find by people who are sympathetic to the goal, the numbers don’t add up,” Clinton told Sanders. “That’s a promise that cannot be kept.”

Sanders said he was simply moving to provide what most industrialized countries have - healthcare coverage for all.

“We’re not going to dismantle anything,” Sanders said. “In my view healthcare is a right of all people, not a privilege, and I will fight for that.”

Sanders also repeated his accusation that Clinton is too beholden to the Wall Street interests she once represented as a U.S. senator from New York, noting her Super PAC received $15 million in donations from Wall Street.

“Let’s not insult the intelligence of the American people,” he said. “Why in God’s name does Wall Street make huge campaign contributions? I guess just for the fun of it, they want to throw money around.”

Clinton said the donations did not mean she was in Wall Street’s pocket, and noted that President Barack Obama had taken donations from Wall Street during his campaigns.

“When it mattered, he stood up and took on Wall Street,” she said.

Slideshow ( 15 images )

THE JUDICIAL SYSTEM AND RACE

With an eye to on the minority vote, both candidates decried the high incarceration rate of African-Americans and called for broad reforms of the criminal justice system. Sanders said the disproportionately high rate of incarceration for black men was “one of the great tragedies” in the United States.

He called for “fundamental police reform” that would “make it clear that any police officer who breaks the law will in fact be dealt with.”

Clinton criticized what she called “systemic racism” in education, housing and employment. “When we talk about criminal justice reform … we also have to talk about jobs, education, housing and other ways of helping communities of color,” she said.

They both agreed on the need for immigration reform, an important issue to Hispanic voters, though they clashed over the Obama administration’s actions on handling a wave of undocumented children who entered the country alone. Clinton criticized Sanders for voting against a reform measure in 2007, which Sanders defended because of a provision in the bill for guest workers.

Clinton entered Thursday’s debate under acute pressure to calm growing nervousness among her supporters after her drubbing in New Hampshire and a razor-thin win the prior week in the Iowa caucus. Both states have nearly all-white populations.

For his part, Sanders, who calls himself a democratic socialist, hoped to harness the momentum and enthusiasm he gained from the first two contests and prove he can be a viable contender to lead the Democratic Party to victory in the Nov. 8 presidential election.

“What our campaign is indicating is that the American people are tired of establishment politics,” Sanders said. “They want a political revolution.”

Clinton dodged an opportunity to distance herself from former Secretary of State Madeleine Albright’s recent controversial comments that there was “a special place in hell” for women who don’t support other women.

“Look, I think that she’s been saying that for as long as I’ve known her, which is about 25 years. But it doesn’t change my view that we need to empower everyone, women and men, to make the best decisions in their minds that they can make,” she said.

On the foreign policy front, Sanders criticized Clinton for her warm relationship for Henry Kissinger, who served as secretary of state under Republican President Richard Nixon during the Vietnam War. Sanders called Kissinger “one of the most destructive secretaries of state.”

Asked by Clinton about who his foreign policy advisers were, Sanders shot back: “Well it ain’t Henry Kissinger.”

The race now moves to what should be more favorable ground for Clinton in Nevada and South Carolina, states with more black and Hispanic voters, who, polls show, have been more supportive of Clinton so far.