The documents, revealed earlier this week, showed how scores of well-known, wealthy figures have used secretive offshore jurisdictions to hide billions of euros.
Eleven million documents were leaked from the Panama-based law firm Mossack Fonseca, in the latest international scandal to lift the lid on the murky world of financial secrecy and tax dodging.
Commenting on the revelations, Tove Maria Ryding, tax justice coordinator at the European Network on Debt and Development (Eurodad) said: "The Panama Papers have given us another peek into the world of dirty money, fake company structures and hidden bank accounts."
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"Unfortunately, it's no surprise that this dark financial underworld still exists. While there have been plenty of political speeches about ensuring transparency and putting an end to tax dodging, corruption and secret shell companies, it hasn't always been matched by political action. People who want to hide dirty money still have plenty of opportunity to do so.
"If countries introduced registries where the public can see who owns the companies operating in our societies, it would make it impossible to set up fake companies to hide dirty money."
Eurodad is now urging the EU and world leaders to:
- Introduce public registers of beneficial owners of companies and similar legal structures.
- Commit to automatically exchange financial account information, ensuring that all countries - including the world's poorest - can receive the information needed to stop tax dodging.
- Take serious steps to address the banks and lawyers that are a key part of the international offshore industry.
On Wednesday, Pierre Moscovici, the EU commissioner for taxation, said the EU has "a duty" to stop the kind of tax avoidance uncovered in the Panama Papers scandal.
Moscovici told reporters the use of offshore companies to hide what he called "shocking amounts" of financial assets from tax authorities was "unethical."
He estimated that the tax shelters resulted in an annual loss of some €1 trillion in public finances.
"It is too early to comment on specific cases," said Moscovici of the information uncovered by the leak. But he added that the Commission has been trying since November 2014 to tighten tax rules across the union and hoped the extent of the Panama Papers revelations would spur countries to action.
The only minister from an EU member state identified in the Panama papers of clients of tax evasion schemes is Malta's health and energy minister, Konrad Mizzi.
Two weeks ago, a Maltese paper reported that Mizzi's Panamanian company and New Zealand trust were both set up on the same day that former Delimara power station consortium partner Gasol sold its shares in the station and earned tens of millions of euros.
On Monday, Malta's opposition leader Simon Busuttil, a former MEP, said that failure to sack Mizzi and Schembri would leave the Prime Minister with no choice but to step down himself.
It has also emerged the UK Prime Minister David Cameron allegedly lobbied then European Council President Herman van Rompuy to water down the effect of transparency rules on trusts despite warnings it could create a loophole for tax dodgers.
The Prime Minister is said to have written to van Rompuy in 2013 in order to argue a Brussels drive to reveal the beneficiaries of companies "may well not be appropriate" for trusts as well.
It comes as Cameron has seen himself dragged into a global offshore tax avoidance scandal following the leak of the so-called 'Panama Papers', which are reported to include details about the Prime Minister's late father.