Russian protest group and musical act Pussy Riot claimed responsibility for a protest which saw three people invade the pitch during the World Cup final at Luzhniki Stadium on Sunday.

Posting on their official Facebook page, the group said: "Just a few minutes ago four Pussy Riot members performed in the FIFA World Cup final match."

According to Reuters, a member of the Anti-Kremlin band, Olga Kurachyova, was one of the people that breached security and entered the field in the 51st minute of the match.

The group's social media post said they were protesting in order to request that all political prisoners be freed, people not be imprisoned for "likes," that illegal arrests at rallies be ended, that criminal accusations not be fabricated, and to turn "earthly policeman into the heavenly policeman," an apparent reference to a Russian poem.

The band is best known for a protest in a Moscow cathedral in 2012 that led to the three members being arrested and jailed. They were also active in the lead up to the Sochi Olympics in 2014.