COPENHAGEN (AFP) - One of the three members of Denmark's leftist coalition quit the government on Thursday over the controversial sale of a stake in state-controlled energy group DONG to US investment bank Goldman Sachs.

"We have followed this DONG case to the end," leader of the Socialist People's Party and minister for social affairs and integration, Ms Annette Vilhelmsen, said at a press conference, where she announced her resignation from both posts.

The party is likely to continue to support Prime Minister Helle Thorning-Schmidt's government in parliament, although it may have to seek support from the opposition on some issues.

At a press conference, Ms Thorning-Schmidt said there was no need to call a new election and that her minority government would "shortly introduce a new cabinet".

"It's the same parliament as yesterday so why should we (have an election)," she said.

"What we do is remarkably different from what a right-wing government would do," she said of her minority coalition.

The Danish government wants to sell a 19-per cent stake in utility DONG to Goldman Sachs for eight billion kroner (S$1.63 billion) after the state utility lost money on natural gas investments.

To pass the deal, the government will have to reach out to the centre-right opposition, just like it did before passing this year's budget.

The deal has drawn ire from grassroot members of the Socialist People's Party, which has been accused of supporting a government whose policies many see as being too right-wing.

Ms Vilhelmsen said she resigned after realising she was unable "to unite the party".

The Social Democratic-led government has cut the corporate tax rate to 22 per cent from 25 per cent, and tightened the requirements for claiming social benefits.

Economic growth in Denmark has been persistently sluggish since a housing bubble burst in 2007, leading to anaemic household spending amid a high level of consumer debt.