"We tell Rumsfeld: you may have escaped unharmed from our swords, but you will not escape again," said "the information office of the Islamic emirate of Afghanistan" in the statement accompanied by footage of Taleban "victories" in Afghanistan.
The statement also promised "a flood of jihad (holy war) ... against the Americans and their allies in Pakistan and Afghanistan."
Two rockets landed in the north of Kabul and in a neighbouring village just hours after a brief visit by Rumsfeld during which he met Afghan President Hamid Karzai on August 11. No one was injured in the attack and one of the rockets failed to explode.
"We give the Islamic nation the glad tidings: jihad in Afghanistan is constantly escalating ... America claims that the mujahedeen are divided ... (But) thanks be to God, the mujahedeen are standing fast and fighting under the banner of (Taleban spiritual leader) Mullah Mohammad Omar," the statement said.