The draft EU legislation seeks to ensure that profits from minerals and metals do not reach armed groups.
The provisional agreement would require mandatory reporting from companies that import the minerals and metals as raw materials into Europe.
These minerals are typically used in everyday products such as mobile phones, cars, washing machines, tablets and jewellery.
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But, under the new rules, only a voluntary disclosure would be sought from those companies importing finished products containing some of the so-called conflict minerals.
This much larger number of companies, such as electronics manufacturers, that use the minerals in their products, would not have due diligence obligation but would be asked to voluntarily disclose details of their sourcing of the minerals.
Amnesty International is among several civil society groups that have criticised this element of the deal, which was agreed last week following talks between the Commission, Parliament and Council.
Amnesty said the new rules fall short of what is required to tackle the problem.
At a briefing in Parliament on Wednesday, Nele Meyer, of Amnesty International, said, "The decision leaves companies that import minerals in their products entirely off the hook. It's a half-hearted attempt to tackle the trade in conflict minerals which will only hold companies importing the raw materials to basic checks."
Her comments were echoed by Iverna McGowan, head of Amnesty International's European institutions office, who said, "The EU has international obligations to protect human rights but went only half way to meet them. EU investors and consumers still won't have any certainty that the companies they deal with are behaving responsibly. This law will change little too little.
"Despite its rhetoric on responsible business, Europe has prioritised profit over people."
Amnesty said that by agreeing to exempt some corporations from the law, the EU has "instead put its faith in the hope that companies will choose to source minerals responsibly without being required to do so."
McGowan added, "This has been tried before, through voluntary standards. These have had minimal impact, as there are still far too few companies taking steps to check their supply chains for conflict and human rights risks."
Maria Arena, a Belgian Socialist MEP who has been involved in the trialogue negotiations, also spoke at the briefing.
She too has voiced reservations about the draft law, saying, "We want clean and responsible trade. That is why we are advocating a binding regulation that applies not only to raw materials, but also to the finished products we consume in Europe.
"But the Council is very resistant to this idea, and has proposed a voluntary system that would only be applicable to companies that import minerals and metals. This position is even weaker than the Commission's proposal. It is just a way for Europe to clear its conscience without having any real impact on the ground or on business practices," she added.
Further comment came from Michael Gibb of Global Witness, who said, "While we recognise the efforts of those, especially within Parliament, who have fought for a Europe in which 'business as usual' means responsible business, we are disappointed the EU has not matched its words with action.
"With EU laws now falling behind those in other countries, the EU is rapidly becoming the weak link in the mineral supply chain. While this (the new agreement) is an important step, the EU should have gone much further to make full use of a unique opportunity to make a real difference."
Parliament previously backed a stricter version of the law, voting in May 2015 for the mandatory due diligence requirements to be extended to all companies using minerals from conflict areas in their products.
The law is largely aimed at Africa, where minerals play a role in several violent conflicts.
The Great Lakes region of the Congo is particularly affected by the phenomenon. Mineral production accounts for an average of 24 per cent of gross national product in African countries and is implicated in no fewer than 27 conflicts on the continent.
Under the new regulations, member states would oversee compliance with the rules and set the size of the sanctions for any companies breaching the laws.
The rules could affect around 900,000 European companies using the metals in auto parts, electronics, packaging, lighting, aerospace, construction, jewellery and other industries.
Conflict minerals are minerals mined in conditions of armed conflict and human rights abuses, mostly in the eastern provinces of the Democratic Republic of the Congo (DRC).
The looting of the Congo's natural resources is not limited to domestic actors - during the Congo wars, Rwanda, Uganda and Burundi are said to have profited from the Congo's resources.
The most commonly mined minerals are cassiterite, wolframite, coltan and gold, which are extracted from the eastern Congo and passed through a variety of intermediaries before being purchased by multinational electronics companies.
The new regulations are expected to be adopted formally in the coming months.