Denmark's government unveiled a major overhaul of its tax agency on Tuesday, after a string of scandals in which billions were lost fuelled public mistrust among citizens whose tax bill is the world's highest.

The changes will partially reverse job cuts in the tax inspectorate made over a decade and will see the current tax authority SKAT replaced with seven regionally-based agencies, Prime Minister Lars Lokke Rasmussen said.

"Enough is enough. We have to restore the Danish citizens' trust in the tax system. That trust is the foundation for our welfare state," Rasmussen told a news conference.

Denmark estimates 12.3 billion Danish crowns ($1.85 billion) were lost to tax fraud between 2012 and 2015.

Danish citizens carry the highest tax burden in the world, according to the Organization for Economic Cooperation and Development, with the total tax take amounting to 47 percent of gross domestic product.

Rasmussen said the overhaul would include 1,000 new positions. The government has cut 4,000 jobs in the tax inspectorate since 2006 as part of money-saving measures.

Copenhagen-based SKAT was created in 2005.

Denmark said last year that it would spend more than $1 billion to upgrade its tax inspection system. It also paid some $900,000 for access to Panama Papers documents in an effort to identify hundreds of suspected Danish tax cheats.

In an effort to recoup money paid out in the form of fraudulent tax refunds to people outside the country, Danish authorities have also carried out raids in Britain and elsewhere. ($1 = 6.6324 Danish crowns)