The Greens member was speaking after the recent first anniversary of the publication of the Panama Papers by the International Consortium of Investigative Journalists (ICIJ).
Giegold used the anniversary to call for closer cooperation on the issue between the authorities of EU member states.
While he declined to name countries, he said that ending of the UK's tax haven business must be a priority during the Brexit negotiations.
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He said, "It is time for member states to stop blocking progress on tackling tax evasion and money laundering."
The mandate of the PANA committee, set up by Parliament to investigate the leaks, has been extended until December. It is expected to adopt its final report in November, after 18 months of investigations.
Giegold, who is a member of the committee, said, "The biggest leak in history made clear what so many had long suspected: just how easy it has been to evade taxes or launder dirty money.
"With the full state of the fraud on display for all to see, the European Commission has been forced to introduce tougher rules against money laundering and is slowly making progress on monitoring tax advisers and the much needed protections for the whistleblowers who make this sort of conduct public."
The deputy went on, "Unfortunately, this will not be enough as long as European governments stubbornly insist on continuing with business as usual.
"Their refusal to progress on public transparency of who owns companies and trusts and delaying tactics on public tax transparency for companies amount to a tacit acceptance of tax dodging. This is an unbelievably short-sighted response to the biggest tax scandal in history."
With negotiations on the EU's draft money laundering directive continuing, Parliament is demanding tougher consequences for offenders.
Giegold said, "Cooperation between the authorities of the member states has to be improved in order to ensure that anti-money laundering rules are truly enforced. Tax advisers, auditors and law firms have to be supervised effectively and whistleblowers to be protected."
The Greens says that the assets of criminals and tax evaders have to become traceable across national borders not only on bank accounts but also in life insurances, funds and real estate.
Giegold said the UK and its offshore territories play a sad key role in the provision of secretive companies.
"As a member of the EU, the UK could block defensive measures to protect the integrity of Europe's financial system. The ending of the UK's tax haven business must become a priority during the Brexit negotiations as a condition for the access to the EU's capital market."