The group's military wing, the Izz al-Din al-Qassam Brigades, said on Saturday it had fired seven rockets, including one at the southern Israeli town of Ashkelon.
Hamas said it carried out the attack in response to Friday's killing of 10 Palestinians in Israeli artillery fire and other raids.
"This is only the start and rocket firings will continue," a spokesman for Hamas's Izz al -Din al-Qassam Brigades said.
"Next time, the rockets will be longer in range and they will hit places deeper inside the Zionist entity. The attacks come in response to the Zionist crimes and the killings of civilians in Gaza," he said.
An Israeli military spokesman confirmed six rockets were fired on Saturday, of which one reached Israeli territory without causing damage or injury.
The Islamist group took power in March after winning Palestinian elections in January.