Istanbul, Turkey (CNN) -- A splinter nationalist group from the Kurdistan Workers' Party has claimed responsibility for Sunday's suicide bombing in Istanbul, Turkey, according to the group's statement on its website.
The Kurdistan Freedom Falcons, or TAK, said the attack, which injured at least 32 people, was "an act of revenge" and carried out by Vedat Acar, who died in the strike.
"We as TAK claim responsibility for the action carried out against the police force of Turkish fascism at Istanbul's Taksim Square on Oct 31, 2010," the statement said.
Acar is described a member of the group's command from Van, an eastern border province populated by ethnic Kurds who have signed up with the Kurdistan Workers' Party, or PKK.
The PKK has been battling the Turkish government since the early 1980s initially for a separate Kurdish homeland.
Kurdistan Freedom Falcons, or TAK, was labeled a terrorist group by the United States in 2008. It claimed responsibility for the bombing of a bus that carried Turkish military personnel and their families in Istanbul. The attack, which occurred in June, killed five people.
More than 30,000 people, mostly ethnic Kurds, have been killed during the fighting between Kurdish militants and the Turkish military. In recent years, rebels say they have given up their demands for an independent Kurdish state and are instead fighting for more linguistic and cultural freedoms.
The Taksim Square bombing occurred the same day that the PKK cease-fire was expected to end, raising suspicions in the Turkish media.
In a statement Tuesday, Turkish President Abdullah Gul called on citizens to stand "in unity against terrorism."
But he also sounded a conciliatory note toward the PKK's cease-fire announcement, saying, "I hope the decision to lay down arms is permanent."
While the PKK has denied responsibility for Sunday's attack and extended its unilateral cease-fire until Turkey's general elections in summer 2011, the Kurdistan Freedom Falcons declared in their statement that they had nothing to do with the cease-fire and their "actions will continue."
On Monday night, a small group of well-wishers placed candles on the pavement in Taksim Square and held a vigil for victims of the attack.