In the statement faxed to The Associated Press, a leader of Hamas' military wing, Izzedine al Qassam, said the two bombers who carried out the attacks were Hamas members Ramez Abu Isleem, 24, and Ihab Abdel Kader Abu Isleem, 20.
"These two operations came as the beginning of our retaliation for the enemy's crimes against our people," the statement said.
Meanwhile, President Bush called on the new Palestinian prime minister to crack down on terrorism.
Israeli warplanes on Wednesday dropped a bomb on the home of a senior Hamas leader, Mahmoud Zahar, wounding him and killing his son and a bodyguard, witnesses and hospital officials said. In all, about 25 people were hurt, including Zahar's wife and daughter.
The bomb hit the Zahar home in Gaza City's Rimal neighborhood, leveling the building and sending huge plumes of smoke into the air. Several adjacent houses were also destroyed. Palestinian police were struggling to control an angry crowd that gathered at the scene.
Zahar, who witnesses said was standing at the front door of his house at the time, was lightly hurt in the leg and was taken to nearby Shifa Hospital. The bodies of the dead were badly burned. Hospital officials identified one of the dead as Zahar's 30-year-old bodyguard. Relatives identified the other victim as Zahar's son, Khaled, 29.
The Israeli military confirmed it carried out the strike and said Zahar was one of the decision-makers behind Hamas' suicide bombings.
It marked the first time Israel went after a Hamas leader in a private home. Hamas said Israel crossed a line -- and vowed to escalate its attacks by targeting Israelis in homes and high-rises.
Hours later, Israeli tanks shelled a Palestinian police post, but no one was injured, Palestinian police and rescue workers said.
Five tank shells were fired at the police post near the village of Karara, east of Khan Younis, but they did not cause any serious damage, police said.
It was unclear why the shells were fired.
The army did not immediately have information on the incident.
As CBS News Correspondent Robert Berger reports, Israeli Prime Minister Ariel Sharon has said that every Hamas leader is marked for death.
A day earlier, Hamas bombers struck a bus stop crowded with soldiers and at a popular Jerusalem nightspot.
Hamas said the bombings came in retaliation for the killing of senior leader Ismail Abu Shanab in a helicopter missile strike on Aug. 21, and "the failed assasination attempt" against Hamas' founder and spiritual leader, Sheik Ahmed Yassin, in a bombing on Saturday.
"We send our greeting to the cells that shared in the implementation of the two operations, and we call upon them to carry out more," the Hamas military wing said. "From now it has become allowed for them to target the Zionists' houses and buildings and to destroy them as retaliation for the enemy policy of targeting civilian houses."
"We hold the criminal enemy responsible for what's going to happen in the future, God willing," Hamas said in the statement.
In one Gaza neighborhood, Palestinians fired assault rifles in the air and about 100 took to the streets in celebration after the attack on the cafe. In the Bureij refugee camp in the central Gaza Strip, some Hamas supporters celebrated by distributing candies to the families of those killed in previous violence.
Israel's military has relentlessly targeted Hamas militants since the group claimed a suicide bombing last month that killed 22 people on a Jerusalem bus.
Before the bombings Tuesday, Israeli troops in Hebron killed two Hamas members — including the group's leader in the West Bank town — and a 12-year-old bystander, and blew up a seven-story apartment building where the militants were hiding out.
After Israel's attack Wednesday on Zahar's house, staff at the hospital called over loudspeakers for people to donate blood to help treat the wounded, who were brought to the hospital in ambulances and private cars. Among the wounded were five children and three women, hospital officials said. Three of the wounded were in critical condition.
Zahar's wife suffered serious injuries but was in stable condition after surgery, said Dr. Hazaa Abed, director of surgery at Shifa Hospital. A daughter of Zahar was also lightly injured. Another of his sons, Sami, was missing.
Zahar himself left the hospital, and Hamas officials said he was taken to a safe place.
After Wednesday's strike, hundreds of students from the Islamic University, where the 58-year-old Zahar is the head of the medical school, gathered at the hospital. Some of them held Hamas banners. Others chanted, "Death to Sharon" and "God is greater than the aggressors."
The violence underscored the collapse of U.S.-backed peace efforts and came amid political uncertainty after the resignation of Palestinian Prime Minister Mahmoud Abbas.
Palestinian parliament speaker Ahmed Qureia said Wednesday he has accepted the post vacated by Abbas.
"I have accepted the appointment," Qureia told reporters after a meeting with Palestinian leader Yasser Arafat. "I will start forming my Cabinet. It will be a crisis Cabinet," Qureia said.
Arafat had tapped Qureia for the job over the weekend, after Abbas resigned following four months of wrangling with Arafat over his authority. Qureia had previously said he would only accept the appointment if he had guarantees that Israel would change its policies.
An increasing number of Israeli officials were calling for the expulsion of Arafat, and expectations were mounting that Israel will step up military strikes and possibly invade the Gaza Strip — which Israel has not yet reoccupied — to root out the Hamas leadership.