Hillary Clinton claimed victory Saturday in the Democratic primary in the southern US state of South Carolina.

With results in for all 46 counties, the former US secretary of state took 73.5 per cent of ballots, over her rival Bernie Sanders on 26 per cent, the state's board of elections said.

It was Clinton's third win in four statewide contests in the race to become the Democratic Party's nominee to run for president in November.

A jubilant Clinton thanked supporters gathered in Columbia, the capital of South Carolina. The former first lady indicated her campaign already is geared up for voting in 12 states on Tuesday and beyond.

"Tomorrow this campaign goes national. We are going to compete for every vote in every state," she said.

She also made a veiled reference to Republican front-runner Donald Trump's slogan "Make America Great Again" and his pledge to build a wall between the United States and Mexico to stop illegal immigrants entering the US.

Clinton said: "We don't need to make America great again. America has never stopped being great. But we do need to make America whole again."

She also said instead of of building walls, the US needs to tear down barriers show each other more love and kindness, admitting that it "seems a little odd that someone running for president in these days and times to say we need more love."

Clinton had been polled to win, but only by 26 points ahead of Sanders.

African-American voters were considered the key to a Clinton victory in South Carolina, and exit polls conducted by television networks showed she won their votes by a margin of 84 to 16.

In conceding to Clinton, Sanders pointed to his overwhelming victory on February 9 in New Hampshire and also looked down the road to voting that will take place Tuesday.

"Let me be clear on one thing tonight," Sanders said in a statement. "This campaign is just beginning. We won a decisive victory in New Hampshire. She won a decisive victory in South Carolina. Now it’s on to Super Tuesday."

He said his grassroots political revolution was growing state by state, "and we won’t stop now."

Clinton won the first contest in Iowa, but it was so close it all but counted as a tie. She defeated Sanders 52.6 per cent to 47.3 per cent in Nevada on February 20.

On the Republican side Trump scored a commanding win in South Carolina on February 20.

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