The incursions forced Aalborg airport, used for commercial and military flights, to shut for three hours, while Billund airport, Denmark's second-largest, was closed for an hour, police said. Both reopened on Thursday morning.
"The Danish government said it's a state activity that operates it," Latvian Foreign Minister Baiba Braze said on the sidelines of the UN General Assembly in New York.
But Danish Defence Intelligence Service chief Thomas Ahrenkiel said at a Thursday evening press conference it was still unclear who was behind the incidents and declined to say if a state actor was suspected.
However, Finn Borch, head of Denmark's national security and intelligence service, told reporters that Russian covert activity poses a security threat.
"The risk of Russian espionage is high. The same goes for the risk of Russian sabotage. We have seen that elsewhere in Europe, and it applies here at home as well," Borch said.
Russia's embassy in Copenhagen on Thursday rejected as "absurd" speculation that Moscow was involved in the Danish incursions.
Denmark's defence minister earlier said the overnight drone sorties were hybrid attacks, combining military and covert tactics, and were aimed at spreading fear.
The incident on Thursday was the second this week in Denmark alone, after drone sightings shut down Copenhagen airport on Monday.
It is part of what some European officials see as a pattern of Russian disruption that has exposed the vulnerability of European airspace at a time of high tensions between Moscow and NATO.
The Latvian minister said Denmark's allies were waiting for further analysis from Copenhagen.
But the incursions have demonstrated "we all have to invest in counter-drone capability," she said.
In Thursday's incursions in Denmark, drones were also seen near Esbjerg and Sonderborg airports, as well as Skrydstrup airbase, home to Denmark's F-16 and F-35 fighter jets, and over a military facility in Holstebro, police confirmed.
They are all located in the western Jutland region.
Danish police said they had increased their presence at the affected airports and other critical infrastructure.
The incursions come after Denmark this year boosted its military budget to address acute shortcomings.
Last week, it announced plans to acquire long-range precision weapons, while its decision to host Ukrainian missile fuel production near the Skrydstrup airbase has drawn criticism from Russia.
Poland shot down suspected Russian drones in its airspace on September 10.
Danish authorities said on Thursday they decided not to take down any of the drones in their airspace for safety reasons, despite the disruption caused to air traffic.
"It certainly does not look like a coincidence. It looks systematic. This is what I would define as a hybrid attack," Defence Minister Troels Lund Poulsen told a press conference.
Denmark has not yet decided whether to invoke NATO's Article 4, which allows members to request consultations over any security concerns, Poulsen added.
Poland invoked the article after downing the drones, as did Estonia after Russian military jets violated its airspace for 12 minutes on September 19.
