The report found that firms including Microsoft, Renault and Huawei have taken "no action" into how the batteries used in their products could be linked to human rights abuses.
But tech giants Apple and Samsung have made some progress, according to the report, which ranked the progress of 29 companies that source cobalt -- a mineral used in batteries for mobile phones and electric cars -- from the world's leading producer the Democratic Republic of Congo.
Children as young as seven were found scavenging for rocks containing cobalt by researchers in the mineral-rich but impoverished vast African country, the report said.
"Cobalt mined by children and adults in horrendous conditions in the DRC is entering the supply chains of some of the world's biggest brands," said the report, which is titled Time To Recharge
As global demand for cobalt skyrockets, the electric car industry is "lagging behind other sectors" the report said under the heading "The dark side of green technology".
Car companies Renault and Daimler have "performed particularly badly", with the human rights group starting an online petition demanding Renault CEO Carlos Ghosn to investigate his firm's cobalt supply chain.
Apple was named an industry leader after becoming the first company to publish the names of its cobalt suppliers this year, but other tech brands have made "alarmingly little progress," including Microsoft, which is "not in compliance with even the basic international standards".
More than 50% of the world's cobalt comes from DR Congo, the report said, with 20% of exports hand-dug by "artisanal miners".
"Amnesty International documented children and adults mining cobalt in narrow man-made tunnels, at risk of fatal accidents and serious lung disease," the report said.
The DRC is one of the world's poorest nations, where 90 percent of its estimated 71-million population lives in extreme poverty.
Competition for its mineral wealth has bred widespread corruption, smuggling and mismanagement, while some funds have been used to fuel armed conflicts raging in the east of the country.