The insurgent group issued the statement in English a day after NATO marked the closure of its combat mission with a low-key ceremony in Kabul, arranged in secret due to the threat of Taliban attack.
"We consider this step a clear indication of their defeat and disappointment," the Taliban said.
"America, its invading allies... Along with all international arrogant organisations have been handed a clear-cut defeat in this lopsided war."
The United Nations said civilian casualties hit a new high this year with about 10,000 non-combatants killed or wounded -- 75 percent of them by the Taliban.
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On January 1 NATO's International Security Assistance Force (ISAF) combat mission will be replaced by a "training and support" mission.
About 12,500 NATO troops will stay on in Afghanistan.
The Taliban statement said the group would fight on "for the establishment of a pure Islamic system by expelling the remaining invading forces unconditionally".