The push comes exactly one year after the European Parliament took a vote on materials that cause violence or conflict to access them.
CIDSE, the international family of Catholic social justice organisations, says that voluntary regulation is not be enough to improve the situation for people living near mine areas around the world.
Jenny Vaughan from Christian charity Progressio told Premier that conflict minerals go into products that many of us use every day like mobile phones or tablets.
Addressing what action they'd like to see, she said: "Ensure that nothing they're putting into their products, any minerals that are going into mobile phones, into lap tops, any technology really, is associated with these minerals.
Ms Vaughan told Premier that a law is needed to do this. She said: "This legislation is really, we feel, the only way to ensure that these minerals are not going to make it into the supply chain and are not going to make it back to the products that we're using now.
"Consumers want to know that the products that they are buying have not caused conflict, violence or devastation.
"We need a mandatory regulation to ensure that all businesses are held to the same standard and have a legal requirement to check their entire supply chains.
"This is the only way to weed out trade practices which are putting people's lives at risk every day, simply because they live close to mines and in mining areas."
CIDSE is welcoming discussions between negotiators - the European Parliament, the European Commission and the 28 EU Member States that form the EU Council.
Together they have agreed to discuss regulation.
CIDSE says that the outcome of these negotiations are still not enough and they want more done to protect locals around mines.
Listen to Premier's Alex Williams speak to Jenny Vaughan here: