The Revolutionary People's Liberation Front (DHKP-C) said on its website that one of its female militants carried out the attack.
It named her as Hatice Asik and said she was later arrested and taken to hospital after being shot by police.
"Our struggle will continue until imperialism and its collaborators leave our country and every parcel of our homeland is cleared of US bases," it said, praising Asik as "our honour".
A Turkish official in Ankara had earlier told AFP on condition of anonymity that the attack "on the consulate is linked with the DHKP-C".
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The group had claimed a 2013 suicide attack at the US embassy in Ankara that left one security agent dead.
Turkish authorities said one of two female militants -- who they had named as Asik -- was captured wounded, and the other was at large.
The Turkish official meanwhile said the outlawed Kurdistan Workers' Party (PKK) was behind a suicide bombing and gun attack on a police station in Istanbul that left three militants and one top police official dead.
Authorities have also arrested more than 1,300 suspects since last month in police raids nationwide targeting suspected members of the PKK, IS group as well as the DHKP-C.
The Turkish official insisted there was no contradiction between Turkey fighting both IS and the PKK, even though the two groups are themselves bitterly opposed.