Nearly 28,000 pages of documents have been leaked, revealing preferential tax treatment given to multinational companies by Luxembourg.
Hundreds of companies, such as Ikea and Amazon, secretly reached deals with the Luxembourgish government to slash their tax bills.
The commission announced in October that it was launching an investigation into questionable tax deals reached between companies and various European governments, including Luxembourg.
These new revelations have placed commission president Jean-Claude Juncker in hot water, as he was prime minister of Luxembourg between 1995 and 2013, during which time some of the tax deals were reached.
During a joint press conference with parliament president Martin Schulz last month, Juncker was asked about the investigation and whether or not he would be involved in the process.
The commission president said he would stay out of the commission's way, but Schulz reminded him of his previous commitment to fight tax evasion and said that he would not let him go back on his promises.
"The credibility of Jean-Claude Juncker is on the line" - Gianni Pittella
Several parliamentary groups have reacted to the publication of the documents, which news outlets have dubbed 'Lux leaks'.
Manfred Weber, chairman of the EPP in parliament, said that his group "fully trusts and fully supports the European commission in the ongoing investigation on schemes in Luxembourg and other member states".
He insisted that the situation is not a personal issue for Juncker, who "has made very clear that, under his leadership, the […] commission would step up efforts to combat tax evasion and tax fraud".
S&D group president Gianni Pittella said that he "will ask the European commission to come to the European parliament next week to explain the urgent action they intend to take in order to fight tax evasion and tax fraud".
He added that it is "no longer acceptable" for governments to come to such agreements with companies, especially at a time when "all governments are struggling to cut their budget deficits […] and have raised taxes for ordinary citizens who cannot escape payment through the sweetheart deals offered to big business".
Pittella believes "the credibility of Jean-Claude Juncker is on the line", and that he must show whether he is "on the side of European citizens or corporate tax dodgers".
Fellow S&D deputy Nessa Childers said that the revelations "deny […] Juncker any moral authority to lecture member states on budgetary discipline".
Guy Verhofstadt, president of the ALDE group, would like the commission to "come to the European parliament immediately to explain if these practices are in accordance with EU law".
He said that his group "[finds] it unacceptable that citizens and SMEs [small and medium sized enterprises] are expected to pay high taxes in this period of crisis, while many in the corporate sector seem to do everything they can to minimise taxes".
He added that "the ALDE group will keep a close eye on the commission with regard to its promise to make progress with a more transparent and fairer corporate tax system in Europe".
Sven Giegold, economic and financial policy spokesperson for the Greens/EFA, said "the fact that […] Juncker served as Luxembourg's finance and prime minister throughout [the period during which the tax deals were arranged] makes him directly complicit in this mass corporate tax avoidance".
According to Giegold, "the commission must now set out a comprehensive action plan against tax dumping", and it is time to reach an "agreement on implementing a binding common consolidated corporate tax base".
He called upon competition commissioner Margrethe Vestager, who is overseeing the investigation into the tax deals, to "give top priority to combating tax dumping".
Meanwhile, Greens/EFA MEP Eva Joly said that Juncker "must act or leave".
The commission president was due to participate in a debate featuring former commission president Jacques Delors, but cancelled his appearance after Delors announced he would not be attending.
The commission has yet to comment on the revelations.