Maftah Ally, the Serengeti district commissioner, said the elephants killed a villager on Friday night when he was guarding his maize farm.
"Three herds of elephants invaded several villages located near the national park and destroyed crops, including maize," said Ally, adding that game rangers from the park were working hard to control the elephants from inflicting more damage.
He added about 150 elephants have since Thursday invaded Kenokwe village, situated 30 kilometres from the national park.
He said villagers spent the whole night trying to control the elephants but to no avail.
Chembo Manyanya, a councilor for Nyamatare ward, said 100 elephants also stayed in Kemugesi village for two consecutive days bringing business in the village to a standstill.
"People could not graze their livestock. They could also not go to their farms fearing the marauding jumbos. Most of them stayed indoors," said Manyanya.
John Lendoyan, the Serengeti District Wildlife Officer, said the game rangers could not control the marauding animals due to lack of facilities, including patrol vehicles.
According to Serengeti district authorities, from 2009 to June 2016, more than 20 people have been killed by elephants and 6,700 hectares of crops have been destroyed by the marauding animals.