Lawmakers in the parliament's Public Accounts Committee said in a statement late Wednesday that they had asked the National Audit Office to investigate a number of issues relating to the sale, including the role of the finance ministry and the company's management in valuing the shares.
The share sale to Goldman Sachs had prompted the leftist Socialist People's Party to leave the former government amid claims that the bank had been given unusually favourable terms.
The issue re-emerged with the June IPO as Dong, still 50.4 percent held by the Danish government, raised 17.1 billion kroner
(€2.3 billion, $2.6 billion) when it listed 17.4 percent of its shares on the Copenhagen bourse.
"We've always been ready to answer any questions that were asked in connection with Dong Energy's capital increase and IPO," chief executive Henrik Poulsen said in a statement.
"We're looking forward to an investigation by the audit office that can illuminate the facts and put an end to the myths and misunderstandings that have been brought forward in the public debate," he added.
Finance Minister Claus Hjort Frederiksen told Danish news agency Ritzau that "the issue has already to a high degree been explored."
The information disclosed included "more than 200 answered questions from parliament and numerous consultations, as well as parliament's finance committee having had access to all key documents."