Survival International reported that the killings allegedly took place last month along the Jandiatuba River in western Brazil but only came to light after gold-miners had boasted of the killings.
It said two gold-miners had been arrested.
Adelson Kora Kanamari, leader of the Warikama Djapar tribe who occupy the Vale do Javari Indigenous land on the border with Peru, said in an interview with the Amazon Real portal that between 18 and 21 people "have been attacked and killed."
"If these stories are confirmed, President (Michel) Temer and his government bear a heavy responsibility for this genocidal attack," Survival said.
Survival also condemned budget cuts to the government's National Indian Foundation (FUNAI).
"All these tribes should have had their lands properly recognized and protected years ago. The government's open support for those who want to open up indigenous territories is utterly shameful, and is setting indigenous rights in Brazil back decades," it said.
A court order last week blocked a decree signed by Temer to open up a huge area of the Amazonian rainforest to large-scale mining.
Speaking to Amazonia Real, Kanamari explained that the situation in the region is "very critical."
"The invaders are landowners, hunters, miners. Many (indigenous) are being killed in isolation, but we don't know the exact dates or number of deaths," he said.
The Indigenous territory of Vale do Javari lies in an area of about 8.5 million hectares , about 1,200 kilometers from Manaus, capital of Amazonas state.
According to FUNAI, there are at least 14 references to isolated Indigenous peoples in the area.
Temer's government has come in for international criticism after rowing back on environmental and indigenous rights policies amid an economic crisis.