"We ... Claim the attack carried by mortar bombs at Istanbul's Sabiha Gokcen airport," on Wednesday, the Freedom Falcons of Kurdistan (TAK) said on its website.
Airport cleaner Zehra Yamac, 30, died of head wounds hours after the blast on the tarmac at the airport on the Asian side of Turkey's largest city.
The wounded victim was also a cleaner.
The attack came as Turkey wages an all-out offensive against the Kurdistan Workers' Party (PKK), which launched an armed insurgency against the Turkish state in 1984, initially fighting for Kurdish independence, then pressing for greater autonomy for the country's largest ethnic minority.
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On its website, TAK lashed out at what it described as a "war coalition" between Turkish President Recep Tayyip Erdogan and the Islamic State group against the Kurds.
It also said the airport attack was a response to the "fascist attacks that turn Kurdish cities into ruins."
The armed group, which had been silent for some time, claimed the attack had inflicted "serious damage" to the airport and that five planes were "heavily" damaged.