The group's military wing, 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 Israeli artillery fire and other raids which killed 10 Palestinians, including women and children on a beach outing.
An Israeli military spokesman confirmed six rockets were fired on Saturday, of which one reached Israeli territory without causing damage or injury.
Sami Abu Zuhri, a Hamas spokesman, confirmed the group would renew its attacks.
"I believe that amid the continued bloodshed of our people and the horrific images of massacres, there is no place for silence."
But Mark Regev, spokesman for the Israeli foreign ministry, said the Brigades' statement meant little because Hamas had been helping other groups to carry out rocket attacks well before Friday.
Israeli air strikes and artillery fire killed 10 Palestinians on Friday, the highest Palestinian toll in a single day since late 2004, Palestinian officials said. Around 35 people were injured.
Among the dead were three siblings aged one, three and 10, along with their parents at a beach in the northern Gaza Strip.
Palestinians said seven people in all were killed at the beach by an Israeli shell. The army said it was too early to be certain.
Two of three siblings killed in the
"This may have been an accident which caused an artillery shell to fall off course, or an older unexploded shell which went off, or perhaps an explosive device which was tinkered with," Major-General Yoav Galant, head of the southern command, said.
He said he was sorry for the loss of civilian life.
Israel said it was investigating whether its forces were responsible for the beach killing in an area it had been shelling to stop resistance fighters from firing rockets over the border.
Dan Halutz, the Israeli military's chief of general staff, later suspended the bombardments.
Israel earlier killed three men in an air strike on what the army said was a rocket crew. Palestinians said they were civilians. Rocket fire had intensified on Friday following Israel's killing of a senior militant the day before.
Ismail Haniya, the Palestinian prime minister, who is also a Hamas leader, called the Israeli beach attack a "war crime" and urged Jordan and Egypt, both mediators in past Israeli-Palestinian talks, to intervene.
Hamas, which has run the Palestinian government since March after winning parliamentary elections in January, spearheaded a bombing campaign during a Palestinian uprising that broke out in 2000.
One of the dozens of injured
Palestinians receiving treatment
On Saturday morning, unidentified assailants killed an officer of the Palestinian Preventive Security in Gaza City's al-Zaytoun suburb, Aljazeera's correspondent in Gaza said.
Palestinian sources said Major Bassem Qutb was gunned down while walking along the city's al-Shabiya intersection.
Afterwards, four people were wounded when supporters of Hamas fired on the car of a top Palestinian security official in Gaza City, witnesses said.
The car of General Rashid Abu Shabak, the Palestinian director of internal security and an Abbas loyalist, came under fire on the sidelines of Qutb's funeral.
A source in the Palestinian security forces confirmed that Shabak's car came under fire. He was not injured in the incident, but an exchange of gunfire between his bodyguards and Hamas supporters slightly wounded three security officials and a civilian, witnesses and medical sources said.
Earlier on Saturday, Maher Miqdad, spokesman for Fatah in Gaza, urged Hamas to take part in political discussions for the sake of reconciliation and agreement.
Speaking to Aljazeera, Miqdad said: "We call on our brothers in Hamas to take part in the talks going on for 50 days, in order to reach an agreement that enables us to be a united, single front [involved] in resistance and political work."
A security official loyal to Abbas
was killed in Gaza on Saturday
At the same, however, Fatah boycotted a meeting between Haniya and leaders of various Palestinian factions, called to discuss the latest Israeli military escalation.
Miqdad explained that Fatah's boycott was in protest against the "killing and kidnapping" by Hamas activists of Fatah cadres.