A man opened fire in a Mormon church in Michigan and set the building ablaze on Sunday, killing at least four people in the latest deadly tragedy that US President Donald Trump called part of a national "epidemic of violence."

Police in the northern US state said the shooter first rammed the church with his vehicle before opening fire with an assault rifle, and then set the building on fire.

The attacker was killed by police in the parking lot eight minutes after the first emergency call came in, Grand Blanc Police Chief William Renye told a news conference.

Renye said that, in addition to two deceased victims announced earlier in the day, two more bodies had been recovered among debris at the burned-down church, with search efforts ongoing.

He said earlier that eight people had also been wounded in the attack, one of whom was in critical condition.

AFP journalists in the adjacent town of Burton saw a large police presence outside the home of the suspected shooter, whom Renye identified as Thomas Jacob Sanford, aged 40.

Renye and other officials did not provide any further details on Sanford. US media reports said he had grown up in the area and was a military veteran.

Images of the aftermath at the Church of Jesus Christ of Latter-day Saints in Grand Blanc, a suburb of the city of Flint, showed most of the building reduced to ashes.

Authorities said the suspect used an accelerant, believed to be gasoline, and set fire to the church "deliberately."

Some suspected explosive devices were found but it was unclear if they were used to start the fire, they said.

Photos also showed the truck apparently driven by the attacker into the side of the building, with two US flags on poles in the vehicle's rear.

FBI Special Agent Reuben Coleman told the news conference that the FBI was now leading the investigation and was looking at the attack "as an act of targeted violence."

Renye said earlier that hundreds were inside when the attack began and that more victims might be found among the debris.

Trump called the shooting "horrendous" and said it was "yet another targeted attack on Christians in the United States of America."

'Epidemic of violence'

The Church of Jesus Christ of Latter-day Saints called Sunday's attack a "tragic act of violence."

"Places of worship are meant to be sanctuaries of peacemaking, prayer and connection. We pray for peace and healing for all involved," it wrote on social media platform X. 

Founded in 1830, the Mormon church considers itself a Christian body but bases its doctrines on the Book of Mormon, a text its followers say contains a fuller version of the words of Jesus Christ than that recorded in the Bible.

Based in the western US state of Utah, there are Mormon churches all over the world, with millions of adherents.

The United States, where firearms are readily available, has a long history of gun violence.

But tensions have soared in recent weeks after a series of high-profile attacks, including the assassination of right-wing activist Charlie Kirk in Utah and a deadly shooting at a federal immigration enforcement facility in Texas.

Sunday's attack also comes a month after a mass shooting at a Catholic church and school in Minnesota, in which two children were killed while attending Mass, and several others were severely wounded.

Political divisions have grown deeper in the wake of the attacks, with Trump launching a campaign targeting left-wing groups he accuses of being "domestic terrorists."

Trump wrote in his Truth Social post Sunday: "THIS EPIDEMIC OF VIOLENCE IN OUR COUNTRY MUST END, IMMEDIATELY!"

The head of the Mormon church, Russell Nelson, died on Saturday at age 101 in Utah, the church earlier announced.

Trump in a separate post said Nelson -- who worked as a heart surgeon before taking on church leadership roles -- was "a physician, literally and spiritually, and will be greatly missed!"