The latest incidents in Danish skies follow similar events in Poland and Romania and the violation by Russian fighter jets of Estonia's airspace, which have raised tensions in light of Russia's ongoing invasion of Ukraine.
Drones were spotted at Denmark's airports in Aalborg, Esbjerg, Sønderborg and at the Skrydstrup air base before leaving on their own, police said.
Billund Airport, the country's second-largest after Copenhagen, was closed for around an hour following unconfirmed reports of drones just after 4am, news wire Ritzau reported.
Aalborg airport, located in northern Denmark, was also shut down before reopening several hours later.
"It was not possible to take down the drones, which flew over a very large area over a couple of hours," North Jutland chief police inspector Jesper Bøjgaard Madsen said about the incident in Aalborg.
"At this time, we have not apprehended the drone operators either," he added in a statement.
South Jutland police said they had "received several reports of drone activity at the airports in Esbjerg, Sønderborg and Skrydstrup", late Wednesday evening.
The Esbjerg and Sønderborg airports were not closed because no flights were scheduled there until Thursday morning.
Police there said the drones "flew with lights and were observed from the ground, but it has not yet been clarified what type of drones they are... or what the motive is."
An investigation was underway with the Danish intelligence service and the armed forces to "clarify the circumstances", police said.
The probe comes days after police said several large drones flew over Copenhagen airport, shutting the facility for hours.
Prime Minister Mette Frederiksen on Tuesday described the Copenhagen incident as the "most serious attack on Danish critical infrastructure" to date.
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"This is part of the development we have recently observed with other drone attacks, airspace violations, and cyberattacks targeting European airports," Frederiksen said.
Moscow has denied being involved in that incident, and rejected accusations from the governments of Poland, Estonia and Romania over drones or airspace violations by fighter jets.
This week's drone incidents follow Denmark announcing it will acquire long-range precision weapons for the first time, citing the need to be able to hit distant targets as Russia would pose a threat "for years to come".
Moscow's ambassador to Copenhagen, Vladimir Barbin, had called the statement "pure madness".
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