EU climate and energy Commissioner Miguel Arias Cañete has "questions to answer" about his possible involvement in the so-called 'Panama Papers' revelations.
The Greens in Parliament say it is "unacceptable that public representatives should be engaged in schemes to shirk their tax responsibilities."
The Spanish official has been named in a huge leak of documents relating to offshore companies.
The revelations came to light after 11 million confidential documents were leaked from the offices of law firm Mossack Fonseca, one of the leading experts and mediators on tax havens.
The documents were leaked to the International Consortium of Investigative Journalists, a Washington-based organisation. They allegedly highlight how a network of lawyers, bankers and other facilitators around the world help the corrupt to hide illicit wealth.
The documents show that Cañete's wife, Micaela Domecq Solis-Beaumont, who comes from the wealthy Domecq family, was empowered to approve financial transactions in Rinconada Investments Group, a Panama-based firm created in 2005.
Rinconada existed while Cañete held public office in Spain and the EU.
Cañete's office reportedly told the ICIJ, a Washington-based body that worked with Sueddeutsche Zeitung, a daily newspaper, on the investigation, that his assets were "administered separately" to those of his wife, and that his declarations were in "full compliance" with the EU's code of conduct.
It is believed that his wife's lawyers also told the ICIJ that "she had declared all of her income and assets to Spanish tax authorities".
On Monday, the Commission chief spokesperson Margaritis Schinas was asked repeated questions about Cañete's involvement as well as that of Ukraine's president, Petro Poroshenko, who is alleged to have set up a secret offshore company in the British Virgin Islands at a time when his troops were engaged in a bitter conflict with Russian troops and pro-Moscow rebels.
Replying to journalists' questions on Cañete, Schinas said his declaration of interests before becoming a Commissioner in 2014 fully complied with EU rules and the code of conduct for Commissioners.
He also said that the company referred to in the Panama Papers "had been active for several years" before Cañete took office .
On Poroshenko, Schinas said the EU had a "structured" relationship with Ukraine but that it still wanted to see what was being done to tackle corruption in the country.
He said the Commission, since taking office, had made tackling tax evasion a priority by taking several initiatives and was satisfied with the work it had done on this so far.
However, it was impossible to speculate on the "scope" of the new revelations.
The Panama Papers, which have led to accusations of shady financial dealings by the leaders of Iceland, Russia and Ukraine, were published by several media on Monday.
They originated in a cache of 11.5 million electronic files belonging to Panama-based law firm Mossack Fonseca that were initially given by an anonymous source to a German newspaper in early 2015.
The list of people implicated in Panama Papers also covers the late father of British Prime Minister David Cameron, the Spanish royal family, the government of former Greek PM Antonis Samaras, a former French minister, a Maltese energy minister, a former Warsaw mayor and a number of British MPs.
Reaction to the possible involvement of Cañete's family came from Green tax spokesperson Molly Scott Cato, who said, "It is unacceptable that public representatives should be engaged in schemes to shirk their tax responsibilities."
The MEP said, "Cañete clearly has questions to answer in this regard and we will be seeking to have him address these revelations in the EU parliament's tax avoidance investigation.
"These latest revelations also highlight the need to finally transform the Parliament's special committee into a fully blown inquiry and we will now push for this. EU governments and the EU institutions have failed to ensure financial integrity, as the major involvement of banks from Luxembourg and the UK in these revelations underlines. This needs to be tackled once and for all."