He described the group as "a terrorist gang that has been exported towards us from Syria".
A faxed statement purportedly from the group claimed responsibility for the blasts and threatened more.
"A group of your heroic jihadist brothers undertook in the last two days ... the planting and detonating of two explosive devices in the heart of Beirut," it said.
"We have warned the government and we have been true to our pledge ... and we have set ablaze and will set ablaze again the heart of Beirut."
"From outside it's very easy to condemn the Lebanese army and government for what they are doing against Fatah-al-Islam"
Rabih, Mansourieh El Metn, Lebanon
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But a spokesman for Fatah al-Islam later denied that the group had anything to do with the bombings.
Syria denied any ties between the government in Damascus and the group.
"We renounce Fatah al-Islam. Members of the group are wanted by the Syrian security services," Walid Muallem, the Syrian foreign minister, said, according to the official news agency SANA.
Shaker al-Abssi, the group's Palestinian leader, slipped in to Lebanon last year after serving three years in a Syrian jail and is the subject of another arrest warrant issued by Damascus.
"This group serves neither the Palestinian cause nor the interests of the Palestinian people," Muallem added.
On Tuesday, Fatah al-Islam itself also denied any links to "parties and states outside Lebanon".