The European Competition Comission will examine the leaked documents
Fine Gael MEP Brian Hayes has called on Mossack Fonseca to testify before European Parliament.
It follows the publication of leaked documents, which detail offshore holdings of 140 politicians and public officials from around the world.
Some 300 Irish companies are named in the documents.
More than 214,000 offshore entities appear in the leak, connected to people in more than 200 countries and territories.
According to the International Consortium of Investigative Journalists (ICIJ), the files expose offshore companies controlled by the prime ministers of Iceland and Pakistan, the king of Saudi Arabia and the children of the president of Azerbaijan.
It is also claimed they include at least 33 people and companies blacklisted by the US government because of evidence they had been involved in wrongdoing.
MEP Brian Hayes has called on law firm Mossack Fonseca to testify before the European Parliament following the revelations.
"These revelations demonstrate an organised web of financial secrecy which should not be tolerated", he said.
"Companies and wealthy individuals should pay their fair share of tax. We have serious problems if firms like Mossack Fonseca are allowed to use special business structures to hide certain financial activity".
"This is a global problem which affects all countries, including Ireland, and accounts for huge amounts in lost revenue".
"Along with other EPP MEPs, I am calling on Mossack Fonseca to testify before the European Parliament's Special Tax Committee", he added.
This committee was set up in the wake of the Lux Leaks scandal, and it has heard from the world's biggest corporations - such as Apple, Facebook and McDonalds.
"Mossack Fonseca is at the heart of possibly the biggest tax evasion scandal in history", Mr Hayes continued.
He also says he has raised this issue with Commissioner for Competition Margrethe Vestager at a public hearing yesterday.
The commission will now review the documentation to see what further investigation may follow.
In a statement, Panama-based Mossack Fonseca has said: "In operation now for nearly 40 years, Mossack Fonseca has never once in its history been charged with criminal wrongdoing, or even been formally investigated in connection with allegations of the same".
"Unfortunately, several recent stories appearing in a handful of international media outlets might lead some to conclude that the opposite is true".