The European Banking Authority (EBA) said in a statement on Wednesday it was closing its investigation.
"At a vote at its meeting on 16 April 2019 the EBA's Board of Supervisors rejected a proposal for a breach of Union law recommendation," it added.
The rejection blocked any further legal action by the EBA against the Estonian and Danish supervisors and signaled EU states' reluctance to let the bloc's authorities investigate the exposure of their banking systems to financial crime.
Danish and Estonian financial regulators have publicly blamed each other for the Danske Bank money laundering scandal, after Denmark's largest bank last year admitted that 200 billion euros ($226 billion) of suspicious transactions flowed through its Estonian branch between 2007 and 2015.
The EBA in February opened a formal investigation into a possible breach of EU law by the two regulators over the Danske case, which is considered by many Europe's largest money-laundering scandal.
All 28 national supervisors but one who sit on the watchdog's board rejected the EBA's recommendation, German MEP Sven Giegold told Reuters after talking to a person familiar with how the decision was taken.
The EBA declined to elaborate on the decision of the board.
The Danish and Estonian financial regulators were not immediately available for comment.
Giegold, who sits in the EU parliament's committee on financial crime, called the decision "scandalous" and urged the EU Commission to continue the inquiry into a possible breach of EU laws by the Danish and Estonian authorities.
"We cannot accept the biggest money laundering scandal in Europe not being properly investigated," he said.
EU states have halted a reform of the powers of EU financial supervisors which was intended to make it more difficult for states to block EU probes into a national supervisor. A watered-down overhaul was definitively adopted on Tuesday.
Earlier on Wednesday the Director General of the Danish FSA Jesper Berg said he was satisfied with the closure of the EBA investigation. He said he was strengthening efforts to curb money laundering and financial crime.
The Estonian FSA also said it would continue its fight against money laundering.
The Danske scandal has reinforced calls by EU lawmakers for stronger European oversight of the union's banking sector and tighter scrutiny of the often close relationships between regulators and the banks they oversee.
"Even if no laws were formally breached, this still leaves unanswered whether regulators lived up to their responsibility and reacted to any suspicions," said Jeppe Kofod, a Dane who heads the European Parliament's Special Committee on Tax Crimes, Tax Evasion and Tax Avoidance.
Danish lawmakers have increased penalties for money laundering eight-fold, and the government says it plans to create a "more aggressive financial regulator".
Adding to the pressure on European lawmakers is an investigation into Swedish lender Swedbank by Swedish and Baltic financial watchdogs after broadcaster SVT reported it processed gross transactions worth up to 20 billion euros ($22.6 billion) a year from high-risk, non-resident clients, mostly Russians, through its Estonian branch between 2010 and 2016.
(Reporting by Jacob Gronholt-Pedersen in Copenhagen and Francesco Guarascio in Brussels, additional reporting by Huw Jones in London; editing by Louise Heavens and Alexandra Hudson)
By Jacob Gronholt-Pedersen and Francesco Guarascio