Member states have also been criticised for refusing to divulge key documents requested by the investigation committee on the Panama Papers, set up by Parliament to probe the scandal.
Speaking at a news briefing on Thursday, German Greens MEP Sven Giegold said, "There has been a complete lack of transparency and cooperation with the committee on the part of both the Commission and Council.
"Both have been terribly slow to respond to our requests for documents needed for the committee to work and this is quite unacceptable."
The committee, chaired by Werner Langen, a German MEP, was launched in July, following the revelation of the Panama Papers, a series of documents exposing the complex financial structures used by certain wealthy people to hide their money in the tax haven of Panama.
MEPs are investigating the ways in which money laundering, tax evasion and tax avoidance are made possible in the EU. Members of the committee are also looking at who is responsible, and how these issues can be tackled.
The committee is due to complete its work by the summer and preparations for the final report are now underway.
This month, MEPs will set off on various missions, including to the UK and Malta.
Giegold, a member of the committee, said an interim report on its findings is due to be issued in March.
But he said that given the "lack of cooperation" by the Commission and Council that this would be "impossible".
He said, "The committee wants to find out if there have been any breaches of EU law or maladministration and we are unable to do that because the information we need is being blocked by the Commission and Council.
"All we have had so far is a batch of rather boring documents and not the 'sensitive' ones we requested."
He added, "This is itself a breach of the principle of 'sincere cooperation' enshrined in EU treaties."
He said that documents relating to implementation of the EU anti-money laundering directive, subject to its latest reform, were among those which had been withheld by the two institutions.
"Public interest in this issue remains very high but, no matter how many nice hearings you have and how many people you meet, this is the sort of important information the committee needs to do its work."
Another example of the lack of cooperation, he said, was the recent refusal of Konrad Mizzi, the former Maltese energy minister, to appear before a hearing of the committee.
He added, "My hope is that, with the committee still to conclude its work, we can still push the Commission and Council to cooperate."
His comments were echoed by Molly Scott Cato, a UK Greens MEP, who said, "To be honest, I am disappointed with the way the committee is working and the lack of progress.
"We have had no high profile political figures coming before the committee to be questioned and that is a disappointment.
"All we have had so far are people who are probably unknown outside of the Brussels bubble. The Panama Papers affair scandalised the public but the committee has not had a chance to quiz any of the powerful people involved."
French Greens deputy Eva Joly said the committee would continue to press for top EU officials to appear before the committee before it ends its work.
She said these include climate change Commissioner Miguel Arias Cañete who, she said, should appear before the European Parliament to respond to the accusations of his alleged involvement in the Panama papers scandal and a corruption case in Spain.
Former European competition Commissioner Neelie Kroes should also give evidence to explain her involvement in the scandal, she said.
The Commission or Council were not immediately available for comment.