Fatah al-Islam broke away last year from Fatah al-Intifada, another Palestinian group.
The breakaway group accused the Lebanese government of trying to pave the way for an offensive against the dozen or so camps in Lebanon, which house more than half of the country's estimated 400,000 Palestinian refugees.
It first emerged in the Palestinian refugee camp of Bedawi in north Lebanon.
"If a man had been killed in the Amazon forest, Fatah al-Islam would have been accused of his murder," the group said in a statement.
The bombing on February 13 was a day before the second anniversary of the assassination of Rafiq al-Hariri, the former Lebanese prime minister, whose killing many Lebanese blame on Syria.
Governing coalition leaders said the bombing was designed to deter their supporters from attending a Beirut rally to mark the al-Hariri killing and to bolster their camp against a political challenge by the opposition.
"If a man had been killed in the Amazon forest, Fatah al-Islam would have been accused of his murder"
Fatah al-Islam group statement
The opposition includes Hezbollah and Amal, which are both close to Damascus.
Ghazi Aridi, the Lebanese information minister, said the men had been instructed to carry out the attack before February 14.
"They said that their bosses had asked them to be ready to carry out another operation," Aridi said, adding that the target was to be an office of the Kataeb party, a Christian faction which is part of the anti-Syrian governing coalition.
Pierre Gemayel, a cabinet minister and Kataeb leader, was assassinated in November.
Ain Alaq, the location of the bus bombings, is in the area of Bikfaya, home to Gemayel's father Amin Gemayel, a former president and Kataeb leader.
Syria denies involvement in the al-Hariri assassination and other attacks on anti-Syrian figures which followed.
The bus bombings had been added to a list of attacks being investigated by a UN inquiry into the al-Hariri killing.