"The American administration demonstrates new proof of its flagrant complicity in Nazi Zionist crimes and terrorism," the Ezzedine al-Qassam Brigades said in a statement.
"From now on, the United States proclaims their hostility towards our people and their total bias in favour of the Zionist entity and aggression," it added.
"We condemn this position of the United States in supporting massacres and giving their blessing to terrorism, murder and destruction."
Israeli Prime Minister Ehud Olmert was quoted as telling MPs in Jerusalem on Monday that the army was "preparing for an even more extensive operation in the Gaza Strip" four months after first sending its troops back into the territory.
Asked about Olmert's remarks, US State Department spokesman Sean McCormack refused to comment on Israeli military actions but put the issue in the context of the Jewish state's right to self-defence.
"It's a sovereign state, it doesn't seek or need the permission of the United States to act in its own self-defence," McCormack said. "We don't do stoplights here: Red, yellow or green."
The Qassam Brigades said they were "fully ready to confront the Zionist enemy" in the Gaza Strip which "will always remain a cemetery for invaders".
Two Israeli soldiers and around 260 Palestinians have been killed in the territory since Israel began its extended offensive in a bid to retrieve a captured soldier and stop rocket attacks on the Jewish state.
On Tuesday, an Israeli general was quoted by online news site Y-Net as telling MPs that Hamas had activated a regular armed unit equipped with anti-tank weaponry in the Gaza Strip.

Copyright AFP (Agence France-Presse), 2006