The European Investment Bank (EIB) has been accused of engaging in a hypocritical "cover-up" of its report into allegations of tax avoidance by a Zambian mining firm largely owned by the Swiss commodity trader Glencore Xstrata.

In 2005, the bank – which is owned by EU member states – loaned Mopani Copper Mines $50m (£30m) for the renovation of a smelter to reduce sulphur dioxide emissions.

Six years later, after a leaked audit report suggested that Mopani had avoided paying tens of millions of dollars in local tax, the EIB announced an investigation into the Zambian company. It also halted loans to Glencore, as the company was known, because of "serious concerns" about its corporate governance. Three years on, the bank has yet to share its findings on Mopani.

Eleven NGOs have written to the bank's president, Werner Hoyer, to demand the release of the report, to express grave concerns over "the secrecy surrounding the bank's investigation", and to ask how the delay in releasing the report sits with the EIB's commitment to "the highest possible levels of transparency in all its activities".

The letter continues: "It is now close to nine months since Christian Aid made a formal complaint to the bank about its failure to publish the Mopani-Glencore report. Despite having had this considerable period of time, the bank still has not replied to the complaint. We consider this an inexplicable and unacceptable delay."

The call – signed by Alliance Sud, Les Amis de la Terre, Christian Aid, the Global Alliance for Tax Justice, Counter Balance, Oxfam, the Centre for Trade Policy and Development, Sherpa, Déclaration de Berne, Tax Justice Network Africa and Eurodad – concludes: "We cannot conceive of anything that would justify such secrecy and we therefore urge the bank to reveal the truth by publishing the report as a matter of urgency."

The allegations arose from a leaked pilot audit report commissioned from accountants Grant Thornton and consulting firm Pöyry by the Zambia Revenue Authority. According to the audit, carried out in 2009, an "unexplainable" increase in Mopani's costs between 2006 and 2008 allowed it to minimise its stated profits and lower its tax bill. Glencore Xstrata, which owns 73.1% of Mopani, has consistently denied the allegations and dismissed the audit report as a "flawed" and "incomplete desktop study".

Christian Aid, which has also lodged a complaint against the EIB with the European Ombudsman, said the bank's failure to publish the report amounted to a "cover-up" of what it knew about the Zambian allegations.

"It may be that the bank found Mopani-Glencore to be innocent of the grave tax allegations made against it – or it may be that the bank has evidence that Mopani-Glencore is guilty," said a spokeswoman. "Either way, the bank must share the truth with the rest of the world."

The Tax Justice Network Africa described the EIB's stance as "characteristic of the hypocritical nature of western financial institutions such as the EIB, who in one breath preach transparency but, in another, show no real and genuine commitment to practise these principles".

An EIB spokesman confirmed the bank was aware of the NGOs' letter but said it had never published the results of its internal investigations.

He said: "A complaint process by the bank's independent complaints mechanism regarding the disclosure is currently in its final phase. A decision is expected in the following weeks. The EIB is also aware of the complaint being handled by the European Ombudsman on this matter. The bank will naturally co-operate with the European Ombudsman in the handling of this complaint."

Glencore Xstrata declined to comment on the EIB's behaviour but pointed out that it had welcomed the launch of the investigation in 2011 and had repeatedly rebutted the allegations which, it said, were based on "fundamental factual errors".