The attack was carried out by Ali Munir Yusuf Jihara, a 24-year-old policeman from the Ayda refugee camp in the Bethlehem region, the group said.
He was the nephew of Jihad Jihara, one of 13 Palestinians expelled to European countries after a siege at Bethlehem's Church of the Nativity in May 2002.
Ten people were killed as well as the bomber when an explosion ripped through a bus travelling close to Israeli Prime Minister Ariel Sharon's official residence in central Jerusalem, during the morning rush hour on Thursday.
Earlier, Palestinian resistance groups Hamas and Islamic Jihad said the blast was justified, without claiming responsibility.
Palestinian prime minister Ahmed Quraya for his part condemned the attack as part of a cycle of violence, calling for a ceasefire in the Israeli-Palestinian conflict and implementation of the moribund road map peace plan.
Officials linked it to the killing of eight Palestinians, including four fighters of Islamic Jihad, which promptly vowed revenge, during an Israeli raid on Wednesday into the Gaza City suburb of Al-Zeitun.
"This attack is a legitimate response of our people to Israeli massacres, including the latest yesterday at Al-Zeitun", Hamas official Said Siam told AFP.
At least eight Palestinians were
killed in Gaza raid on Wednesday
"The author of this attack, whoever it is, defends the rights of our people," Siam added.
"The enemy must know that the resistance will not stand by in the face of aggression and occupation and our people will retaliate."
Islamic Jihad leader Muhammed Al-Hindi said, "Israel bears responsibility for everything that is happening. Yesterday a massacre took place in Al-Zeitun and no one condemned it, but today we will hear condemnations from all sides internationally and calls to strike at the resistance".
"It is Israel which always begins the cycle of violence and our people have the right to defend themselves."
Palestinian premier, Ahmad
Quraya's (R) office criticised blast
A statement from Quraya's office said, "The prime minister condemns the cycle of killings, liquidations and attacks aimed at civilians on both sides."
"What happened yesterday in Gaza and today in Jerusalem confirms the need for an intensification of international efforts to advance the peace process, Palestinian negotiations minister Saib Uraiqat told AFP.
Palestinian interior minister Hakam Balaawi also condemned the Jerusalem blast, while accusing the Israeli government of "relaunching the cycle of violence" with its incursion on Wednesday.
Humiliation of Palestinians
In a statement Balaawi warned Israel against "any act of vengeance against our people and their legitimate leadership," saying that it would bring more violence.
Earlier Palestinian ambassador to the Arab League Muhammad Subaih, speaking on Egyptian television, said the explosion was "a message proving that only the recognition of the rights of others can guarantee peace and security."
Palestinians say separation barrier
does not bring security
"The separation walls, and massacres like the one in Gaza, do not bring security," Subeih said, stressing that the bombing took place near the residence of Israeli Prime Minister Ariel Sharon.
"Walls and massacres, as well as the humiliation and destruction of the property of Palestinians can only bring more violence and operations like that which took place this morning," he added.
Subaih denounced what he said were Israeli efforts to "throw the blame for the attack on the Palestinian Authority before even having identified the culprits."