Expressing deep concern about violence tied to white supremacy and other forms of bigotry, Gov. Andrew M. Cuomo proposed on Thursday to make New York the first state to classify “hate-fueled” killings as domestic terrorism.

Mr. Cuomo, a Democrat, unveiled the proposal in a speech, almost two weeks after back-to-back massacres in El Paso, Tex., and Dayton, Ohio, prompted all-too-familiar cries for action from both political parties.

Describing the need to address the “new violent epidemic” of “hate-fueled, American-on-American terrorism,” Mr. Cuomo called for raising the penalties for violence motivated by race, gender, sexual orientation or other protected classes by making them punishable by up to life in prison without parole.

“Today, our people are three times more likely to suffer a terrorist attack launched by an American than one launched by a foreigner,” he said. “Now this is not just repulsive. This is not just immoral. This is not just anti-American. It is illegal. And we must confront it by enacting a new law to fit the crime.”