At least 20 people have been killed in a stampede during a church service in the northern Tanzanian town of Moshi, according to officials.

The tragedy happened on Saturday while hundreds of worshippers were attending a prayer ceremony led by Boniface Mwamposa, a popular preacher who heads the Arise and Shine Ministry Tanzania.

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The stampede occurred when Mwamposa, who calls himself the "Apostle", poured what he said was holy oil on the ground and the crowd surged forward to touch, hoping to be cured of sickness, according to witnesses and officials.

"Twenty people died and 16 others were injured in the incident," Kippi Warioba, Moshi district commissioner, told Reuters news agency by telephone. Five of those killed were children, he said.

"The stampede occurred when the worshippers were rushing to get anointed with blessed oil," Warioba added.

Authorities said they were still assessing the situation amid fears the death toll could rise.

"The incident took place at night and there were many people, so there is a possibility that more casualties could emerge," Warioba said.

Peter Kilewo, a witness, described the scene as "horrible".

"People trampled on mercilessly, jostling each other with elbows," he told AFP news agency. "It was like the preacher had thrown bundles of dollars about ... and there were all these deaths!"

Tanzania has seen an increase in the number of "prosperity gospel" pastors in recent years, who promise to lift people out of poverty and perform what they call miracle cures.

Thousands of people in the nation of 55 million flock to Pentecostal churches, whose main source of income is the "tithe", the 10 percent or so of their income that worshippers are asked to contribute.