"In this case, of course, it is interesting to understand, what is Russia? Russia is a country, and Russia does not engage in hacker attacks," Peskov told reporters.
He further asserted that more needs to be done to understand "what is at issue and what was the basis for these statements."
The spokesman said the Kremlin was unaware if Denmark had made any requests to Russia with regard to the matter, adding that the Foreign Ministry would be better informed.
The Danish claims are the latest in a long line of cyberattack allegations concerning Russia that have been made by Western politicians over the past several months.
The trend was started in the United States, where Russia was accused of hacking in an effort to influence last year's presidential elections, while in France, independent presidential candidate Emmanuel Macron's campaign accused Russia of targeting his En Marche! party's servers ahead of this year's presidential election. In the United Kingdom, the Government Communications Headquarters (GCHQ) has issued warnings that Russia may try to interfere in the 2020 general election. Russia has rejected all such claims as groundless and made without a shred of definitive evidence.