Revolutionary Struggle emerged four years ago. Its rocket-propelled grenade attack on the embassy has made it Greece's biggest security threat since the dismantling of the November 17 group in 2002.
While the heavily-guarded building sustained only minor damage, police fear that the pre-dawn strike marks the start of a new cycle of violence.
The proclamation sent to the paper condemned US foreign policy, mainly in Iraq and the wider Middle East, and the Greek government as a "blind" US ally.
The group said its embassy attack was dedicated to Iraqi "resistance which is crushing the US war machine", saying it had made many Lebanese, Iraqis and Palestinians happy.
"Our attack against the US embassy is a message that not only is Greece not aligned to this established order but there is also a battle. There is an armed battle against the New Order."
It mentioned Byron Polydoras, Greece's public order minister, and Dora Bakoyanni, the foreign minister, who rushed to the embassy soon after the attack to condemn it, calling them "praetorians" of the US government.
Revolutionary Struggle has in the past bombed the Greek economy ministry and the Athens court. It also tried to assassinate George Voulgarakis, the culture minister, with a bomb last summer.
No member of the group has ever been caught.