Jørgensen ordered an investigation of the issues following pressure on Monday from the minority government’s allied parties.

“We think it will be good to get a clear idea of it. That’s what I have asked my agency to investigate now,” Jørgensen told broadcaster TV2.

The investigation will take the form of a “critical inspection”, TV2 writes. It is unclear how this will be conducted.

Jørgensen earlier said that the government had no plans to investigate the matter.

The 6,000 kroner cheques were intended to offset skyrocketing energy costs for households heated by gas ahead of winter. But due to inaccuracies in an online database that requires homeowners to self-report information on their home, including gas boilers, many people are believed to have received the cheques in error.

READ MORE: Danish parties urge investigation of heating cash sent to ineligible homes 

The one-off payouts, agreed by parliament in March, were sent earlier this month to over 400,000 households which meet the criteria set to receive the relief.

Households with a collective pre-tax income of under 706,000 kroner were eligible for the one-off cash boosts. Additionally, the household should be primarily heated by individual gas heaters, electronic radiators or be located in a district heating area in which the heating is produced by at least 65 percent gas.

However, concerns were raised that some ineligible households had received the payment. The government used an online database that relies on self-reported information from homeowners (which must also be confirmed by municipalities) to determine who was eligible.

Inaccuracies in the database meant some households that have since switched from gas to another heat source, or have even moved to a different residence altogether, received the cheques in error. 

The legislation approving the cheques explicitly stated that households that received the cheques despite not being eligible wouldn’t be required to return the money.

But some reports have quoted critics, among them some who received the money in error and have tried to return it, concerned over a needless waste of tax kroner. 

The scheme has cost the government 2.4 billion kroner.