Luxembourg's Prime Minister Xavier Bettel is in "serious but stable" condition with COVID-19 and will stay in hospital for two to four more days, his government said Monday.

A source in the 48-year-old's office told AFP that Bettel "is short of breath, but not intubated".

The Luxembourg premier received one dose of the AstraZeneca coronavirus vaccine on May 6 but, as one of Europe's younger leaders, has not received his second jab.

Bettel went into voluntary self-isolation on June 27 with mild COVID symptoms. He was then hospitalised on Sunday for what was announced as a 24-hour precautionary measure.

"At that time, insufficient oxygen saturation was diagnosed, and the prime minister has been under continuous medical observation since then," the government statement said.

"The prime minister's current medical condition is considered serious, but stable," it said. 

"The medical staff attending the prime minister therefore decided that hospitalisation is still necessary at this time to continue observation for an estimated period of two to four days." 

Finance Minister Pierre Gramegna, a fellow liberal, will be given authority to ensure government continuity but Bettel is able to coordinate most business from hospital.

Bettel's symptoms began less than 48 hours after he returned from a summit of the 27 European Union leaders in Brussels, but none of the others have been named as at risk of exposure.