The demand comes after Parliament's Greens/EFA group published what it says is new evidence of alleged tax evasion by Inditex, the group that owns fashion giant Zara.
According to the Greens, Inditex saved nearly €600m in taxes between 2011 and 2014 by using "aggressive corporate tax avoidance techniques."
This, it is claimed, took place in Ireland, the Netherlands and Switzerland, three of the countries where Inditex has a base.
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In Ireland, the group uses Irish subsidiaries which are only taxed at 12.5 per cent. In the Netherlands, where it also has a subsidiary, the corporate tax rate is just 15 per cent.
Research carried out by the Greens says the group saved tax amounting to €378.42m in the Netherlands and €58.27m in Ireland.
The report, published in Parliament on Thursday, said, "The purpose of this report is not to shame Inditex or Zara but to illustrate the mismatches and gaps in European and national tax law which practically guarantee that multinationals will adopt aggressive tax avoidance strategies."
It says the aim of the investigation is to "raise awareness of these issues to foster change at European level."
The information, which comes at a time when US multinationals Alphabet, Amazon, and Apple are also feeling the heat in Europe, will feed into the work currently being done by the special parliamentary committee set up to investigate the so called Panama Papers scandal.
Speaking at a news conference in Parliament, British MEP Molly Scott Cato called for an end to what she called "tax shopping" that, in this case, allows Zara to take advantage of the tax regime in Ireland where the corporate tax rate has fallen from 30 per cent in 1996 to 12.5 per cent today.
"This is a stark example but illustrates the need for minimum tax rates at the EU wide level in order to stop this type of tax shopping," she told reporters.
Bas Eickhout, a Dutch Greens MEP, said, "As seems to always be the case in these tax avoidance issues, my country is among those being highlighted.
"The report shows how big companies are shopping around to avoid paying tax in the country where they are supposed to do so."
Ernest Maragall, a Spanish Greens deputy, said one of the problems that need addressing is that many companies do not disclose enough information to their national tax authorities.
He said, "We don't have enough transparency on tax disclosure, which is one reason why we need mandatory public country-by-country reporting of key financial data. This would enable users of financial statements to assess whether taxes paid by multinationals in each country are in alignment with their substantive economic activities."
His colleague Ernest Urtasun also called for minimum corporate income tax throughout the EU.
"We are not talking necessarily here about fraud but tax evasion and this is a battle for all Europe. Reforms have to come in quickly so that big companies pay their taxes."
The report is the third drafted by the Greens/EFA group.
In the recent past, it put Ikea under the microscope for corporation tax avoidance.
The Swedish furniture company has been accused of avoiding more than €1bn in taxes over the past six years.
According to the Greens, the company has funnelled much of its sales through tax havens on the continent.
Meanwhile, the group has previously said that the German chemicals giant BASF used aggressive tax strategies to avoid paying €923m in taxes over a five-year period.
The issue hit the headlines in August, when the European Commission ordered Ireland to recoup up to €13bn in unpaid taxes from Apple. Dublin and the US technology giant are fighting the decision.