A statement that was faxed to news organizations said, "Al-Quds Brigades brings to our people and nation the good news of the arrival of its first martyrdom to the heart of Baghdad."
"This is to fulfill the holy duty of defending Arab and Muslim land," it said.
The group's Lebanon representative, Abu Imad al-Rifai, confirmed the statement to Reuters News Agency. He said the suicide bombers had not come from Palestinian territories but from several countries.
The group, which the U.S. government lists as a terrorist organization, also claimed responsibility for Sunday's suicide bombing in a crowded pedestrian mall in the Israeli seaside town of Netanya. The bombing wounded at least 30 people.
The bomber set off his explosives studded with nails near a group of Israeli soldiers, after a security guard prevented him from entering a crowded cafe, police and witnesses said.
The attack was the first of its kind in almost a month. In a telephone call to the Associated Press, Islamic Jihad identified the bomber as a resident of the West Bank city of Nablus. The attacker died, and at least six of the wounded are in serious condition, hospital officials said.
Israel's police minister, Tsahi Hanegbi, suggested the attack was linked to the war in Iraq. "The [Palestinian] motivation to harm Israel and to help the Iraqi struggle is well known to us and it comes across in all the intelligence reports," he said.
Another Palestinian militant group, Hamas, said earlier it would focus its fight against the Israeli occupation of Palestinian territories, and not what is going on in the rest of the world.
Saeb Erekat, a Palestinian Cabinet minister, said the Palestinian leadership "condemns targeting civilians, whether Palestinian or Israeli." He said the bombing highlights the need for the U.S., Russia and Europe to revive talks aimed at implementing the peace plan outlined earlier this month by U.S. President Bush and British Prime Minister Blair.
That plan includes halting Israeli settlements in the Palestinian territories and creating a Palestinian state by the year 2005.
However, Sunday's attack and Islamic Jihad's announcement that they have sent suicide bombers to Iraq poses a challenge to Mahmoud Abbas, the new Palestinian prime minister. The U.S. has stated that it wants Abbas, also known as Abu Mazen, to rein in Palestinian militants. Abbas was meeting with Palestinian factions in Gaza Sunday.