The bill has been criticized by the West as placing unacceptable restrictions on the work on domestic and foreign NGOs, seen as one of the few sectors still outside direct government control.
The bill means civil groups will be subject to much stricter controls, including greater scrutiny of their funding.
Emma Udwin, a commission spokeswoman, welcomed amendments that softened the original version of the bill.
But she told RFE/RL on 23 December in Brussels that the draft law is still problematic.
“There have been some amendments made to the original law that was put forward, and those changes go in the right direction," Udwin said. "We still would have preferred that this law had never been brought forward at all, but these changes make the situation better than it looked at the outset. We will now try to work within it, keeping the situation under review."
Russia argues the law is necessary to fight terrorism and control attempts by other countries to influence Russian politics.
Last week, however, EU commissioner Guenter Verheugen told the European Parliament the draft law as it stood then was not “proportionate” to these concerns.
Udwin indicated the EU's initial “deep concerns” are yet to be assuaged.
The bloc channels most of its aid money to Russia through NGOs. So the bill, Udwin says, could hamper the EU's work.
“We did have some very deep concerns at the outset that this would make it extremely difficult for us to achieve some of the objectives that we are indeed discussing with our Russian partners -- we work with NGOs to implement some of our programs and projects," she said. "We do think that the changes that have been made make this more liveable, [but] it's not ideal, we would have preferred that there should have been no law of this kind at all.”
Last week, the European Commission warned the bill may damage its 20 million euro ($23.7 million) social rehabilitation program in Chechnya, where the EU is the largest aid donor.
Udwin said today the program will go ahead, but said it is impossible to predict the impact of the proposed law.
“We will go ahead, as planned, with the activities that we have wanted to launch in the Northern Caucasus," Udwin said. "This about trying to improve the living conditions in that part of the world by supporting health, education, and other general basic services. That will certainly go ahead. Now, we will have to see how these new rules affect our activities. I think it is unlikely that there will be no effect, but as I’ve said, we do think that the changes that have been made make this a somewhat more liveable-with situation, and we will have to do our best within the new rules.”
Verheugen last week also warned Russia that NGOs play an important part in maintaining a vibrant civil society, which is essential for sustainable democracy.