The group, which calls itself NoName057(16), has previously announced attacks against Danish sites.
According to DR, eight parties have been affected, as has the English-language site The Copenhagen Post.
Last week, several Danish municipalities were hit in the same way. Danish authorities have concluded that the pro-Russian group was likely behind it and that it has a connection to the municipal and regional elections, which are being held on Tuesday.
The group regularly carries out denial-of-service attacks against sites in various European countries in connection with elections, Danish authorities say.
