Denmark made the proposal during a meeting of EU environment ministers in Luxembourg.
"We need to acknowledge that we are in a bit of a hurry," Danish Climate and Energy Minister Dan Jorgensen told Reuters after the meeting.
He said the diesel and gasoline-powered car ban will hopefully put pressure on the Commission to propose a phasing out of fossil fuel-powered vehicles in the bloc in the coming two decades.
Denmark made headlines in October 2018 when its government announced that it would ban the sale of all fossil fuel-powered cars by 2030, but it subsequently scrapped the idea because this would have breached EU rules.
Jorgensen said if the EU could not agree on a union-wide ban, it would be good if individual countries were allowed to implement such a measure.
"Plan A would be to make it a European ban," he said.
Jorgensen said it was important to communicate the bloc's long-term policy directions to carmakers and that Denmark's next step was to set up an alliance with the 10 member states that support its proposal.
"Then I think others will follow," he said.