The Electoral Commission is refusing to apologise after a watchdog ruled it had failed to properly investigate a Lib Dem donor later convicted of fraud.
Michael Brown gave the party £2.4m in the run up to the 2005 election - its biggest ever gift from an individual.
The party was allowed to keep the cash in 2009 after an investigation by the commission.
The Parliamentary Ombudsman said the commission "did not make adequate inquiries of the party".
Conservative MP John Stevenson said he had asked the ombudsman to investigate the Electoral Commission's handling of the affair after a complaint from a constituent.
The Ombudsman reported: "The Commission failed to seek relevant evidence at the outset, failed to give an informed view on the matter and failed to review the position on the receipt of new evidence."
Initial checks "fell significantly short of what was required" about donations in cash and also flights, the Ombudsman said.
"It failed to ask for relevant information without good reason and so failed adequately to discharge its monitoring function," the Ombudsman continued.
"That was maladministration.
"The commission did not follow up the concerns that it had about the robustness of the checks the party had made as it had said it would.
"That was maladministration."
But the commission has refused to agree to the Ombudsman's demand for an apology.
It disputes the findings and has agreed only to set out the lessons that have been learned from the case and to review the adequacy of subsequently-published guidance on what constitutes "carrying on a business" and what checks a party should carry out.
Labour's shadow Cabinet Office minister Michael Dugher called on Lib Dem leader Nick Clegg to "come clean" and pay back the money.
He said: "Nick Clegg and the Liberal Democrats have justified their inaction against the convicted fraudster Michael Brown by hiding behind a report which has now been totally discredited.
"For years Clegg has dodged questions on when the Lib Dems will pay back the donations. Clegg has nowhere now to hide. He should do the decent thing and pay back this money straight away."
UKIP leader Nigel Farage, who claims his party has been "hounded" by the Electoral Commission "on matters of no substantive basis", called for it to be scrapped and replaced "with an organisation that is fit for purpose".
Brown, 46, donated £2.4m to the Lib Dems before the 2005 general election, through his company 5th Avenue Partners Ltd.
He was convicted in his absence in November 2008 of stealing $8.5m (£5.2m) after posing as a highly successful bond dealer, who claimed connections with royalty.
Brown went on the run to the Dominican Republic in 2008, sparking an international manhunt, after stealing millions from clients including former Manchester United chairman Martin Edwards. He was arrested and then jailed in 2012.
John Stevenson, the Conservative MP for Carlisle, whose constituent took the case to the Ombudsman, said Electoral Commission bosses should be hauled before MPs to explain why they appeared to approve a donation they knew to be made up of money stolen from investors.
He said: "My constituent is rightly outraged at the conduct of the Commission and I believe that the Chair of the Electoral Commission and Chief Executive have serious questions to answer.
"I will certainly recommend that they explain themselves to the Public Administration Select Committee. I will be writing to the Chair of the Committee to make this recommendation.
"Now that the Liberal Democrats know from the Parliamentary Ombudsman's report that they inadvertently benefited from the proceeds of crime, I call on them to voluntarily surrender the money and not be seen to be benefiting from crime."