The human rights group has followed its January 2016 report into companies like Apple, Samsung and HP with an update on how big cobalt consumers are checking on their supply chains.
The results were not good for the carmakers, with Mercedes owner Daimler and Renault failing the supply chain test.
"Demand for cobalt could … be sustaining human rights abuses," said Amnesty's Joshua Rosenzweig.
"As demand for electric cars grows, it is more important than ever that the companies who make them clean up their act.
"Governments also have a role to play here, and should take meaningful action on ethical supply chains, a priority when implementing green policies."
Amnesty said Daimler and Renault failed to meet "even minimal international standards for disclosure and due diligence, leaving major blind spots in their supply chains".
BMW won kudos for making "some improvements to its supply chain" in the past year.
Amnesty has previously said it found children as young as seven working without protection in cobalt mines in the DRC.
Renault said in a letter to Amnesty it followed OECD guidelines and required suppliers to comply with "laws related to responsible procurement of minerals".
Daimler disagreed with the statement it was not doing enough.
"Daimler is by no means ignoring its responsibility in terms of human rights due diligence, as your current statement seems to suggest," Wolfgang Heger from the corporate responsibility division said in a letter to Amnesty.
"On the contrary, we are in the process of building a dedicated human rights due diligence system for our entire supply chains, not only cobalt, on the basis of the UN guiding principles for business and human rights and with reference to the OECD guidance."
Amnesty said tech companies - the main focus from the earlier report - had done better on not buying cobalt mined by children.
Apple has published the names of its cobalt suppliers and worked with Huayou Cobalt to get it from the right places, and Dell and HP have also investigated cobalt sources further.