An arson attack on a historic black church in Mississippi is being treated as a hate crime, police said, after "Vote Trump" was spray-painted on its walls.

Hopewell Missionary Baptist Church in Greenville was set on fire on Tuesday evening and suffered extensive damage, though no one was injured.

Pastor Carolyn Hudson said the incident "left our hearts broken", adding that the church has a 111-year history.

Greenville fire chief Ruben Brown told a news conference on Wednesday afternoon that investigators had determined the fire was "intentionally set".

"Samples and evidence have been collected from inside the church and are being analysed to determine the accelerant or ignition source," Brown said.

Greenville police chief Delando Wilson confirmed the incident is being investigated as a hate crime. "We feel that the quote on the church is intimidating," he said.

"It tries to push your beliefs on someone else, and this is a predominantly black church and no one has a right to try to influence the way someone votes in this election."

Wilson told the Wall Street Journal that police on Wednesday evening were interviewing a "person of interest" in connection with the fire but the individual had not been charged.

The attack comes just a week before the US presidential election on November 8.

Black churches in the US South have long been a base of support for the Democratic Party.

During the US civil rights movement of the 1950s and 1960s, southern black churches were often targets for arson and bombings by white supremacists.

"The FBI Jackson Division is aware of the situation in Greenville, and we are working with our local, state and federal law enforcement partners to determine if any civil rights crimes were committed," the agency said in a statement.

"This act is a direct assault of people's right to freely worship," Greenville Mayor Errick Simmons said in a statement.

The Mississippi Republican Party declined to comment.

In October, the Orange County Republican Party's office in Hillsborough, North Carolina, was set on fire and a graffiti message left nearby said "leave town or else".

No arrests have been made in that incident, which Indiana Governor Mike Pence, the Republican vice presidential candidate, called "political terrorism".

Additional reporting by Reuters.