Mississippi voters are going to the polls to decide the last US senate race of the midterms, as authorities investigate nooses found hanging from the state capitol amid a divisive campaign by the Republican incumbent.

The Mississippi department of public safety is looking for several suspects who hung seven nooses and signs on Monday that referred to the election and the state's history of lynching.

"We're hanging nooses to remind people that times haven't changed," one of the signs reads.

Mississippi's past of racist violence became a dominant theme after a video showed Republican senator Cindy Hyde-Smith praising a supporter in early November by saying, "If he invited me to a public hanging, I'd be on the front row".

If elected, Ms Hyde-Smith, who inherited her seat after her predecessor retired, would be the first woman ever elected to congress from Mississippi.

Either way history will be made, as her Democrat opponent, Mike Espy, would be the state's first African-American senator since Reconstruction.

Noose hangs on a tree on the state capitol grounds in Jackson, Mississippi (AP)

The pair face a runoff on Tuesday after neither won more than 50 per cent of the vote in a special four-way election on 6 November.

After footage of Ms Hyde Smith's comments were aired earlier this month, the 59-year-old apologised to "anyone that was offended by my comments", but also said the remark was used as a "weapon" against her.

Ms Hyde-Smith, an unwavering supporter of Donald Trump, was seen in another video talking about making voting difficult for "liberal folks", and a photo circulated of her wearing a replica Confederate military hat during a 2014 visit to Beauvoir, last home of Confederate president Jefferson Davis.

Critics said Ms Hyde-Smith's comments and Confederate regalia showed callous indifference in a state with a 38 per cent black population, and some corporate donors, including Walmart, requested refunds on their campaign contributions to her.

Cindy Hyde-Smith addresses crowd during rally alongside Donald Trump (AP)

Mississippi — which still has the Confederate battle emblem on its state flag — has a history of racially motivated lynchings. The Naacp website says between 1882 and 1968, there were 4,743 lynchings in the US, and that nearly 73 per cent of the victims were black. It says Mississippi had 581 lynching during that time, the highest number of any state.

Ms Hyde-Smith was in her second term as Mississippi's elected agriculture commissioner when Republican governor Phil Bryant chose her to temporarily succeed longtime Republican senator Thad Cochran, who retired in April amid health concerns. Tuesday's winner will serve the last two years of Mr Cochran's six-year term.

Mr Trump on Monday campaigned with Ms Hyde-Smith and praised her at a rally in the northeastern Mississippi city of Tupelo for voting to confirm Brett Kavanaugh to the Supreme Court.

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"She stood up to the Democrat smear machine," Mr Trump said.

With the Mississippi election undecided, Republicans hold 52 of the 100 Senate seats.

Mississippi last elected a Democrat to the US Senate in 1982, but Mr Espy was trying for the same kind of upset win that fellow Democrat Doug Jones had nearly a year ago in neighbouring Alabama, another conservative Deep South state where Republicans hold most statewide offices.

Mr Espy campaigned as someone who would be able to bridge the partisan divide in Washington. He was endorsed by former vice president Joe Biden, and three Democrats who are potential 2020 presidential candidates — former Massachusetts governor Deval Patrick and senators Kamala Harris of California and Cory Booker of New Jersey — travelled to Mississippi to campaign for him.

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"I ask you tonight, Mississippi. It's the third decade of the 21st century. Why are we still fighting about the colour line?" Mr Espy said during a speech on Monday night at a predominantly African-American church.

"This is a campaign that goes to the colour line and it reached across the colour line, across the chasm of racial division, across the chasm of racial acrimony," Mr Espy said.

If white voters outnumber black voters 2-to-1 on Tuesday, Mr Espy would have to win 30 per cent or more of white votes, a tough task in a state with possibly the most racially polarised electorate in the country. But if black voters rise to 40 per cent of the electorate and Mr Espy wins 9 out of 10, he needs less than a quarter of white votes to squeak out a victory.

"If Espy wins that race, it represents a huge breakthrough for America," said the Reverend Jesse Jackson, a longtime civil rights activist and former Democratic presidential candidate. "If he loses, it's a brief statement about Mississippi being unrepentant."