The US is expecting the Northern Alliance to attack
The Taleban's only foreign envoy, Abdul Salam Zaeef in the Pakistani capital Islamabad, had said it was clear that America was "intentionally targeting the Afghan people".
Mr Rumsfeld also denied Taleban claims to have brought down US helicopters during a special forces raid on Kandahar on Friday. Television pictures of aircraft wreckage have come out of Afghanistan.
"The Taleban have said they have shot down at least two helicopters, which is false. They have not," Mr Rumsfeld said.
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The US campaign against the Taleban began almost two weeks ago after they refused to hand over Osama Bin Laden, the man suspected of masterminding last month's terror attacks on New York and Washington, and key members of his al-Qaeda network.
He confirmed that American aircraft were targeting the Taleban's forces north of the capital Kabul and near Mazar-e-Sharif in support of Northern Alliance forces.
"Our efforts from the air clearly are to assist those forces on the ground in being able to occupy more ground," he said.
"We are happy and eager and willing to do what we can to help seek out and destroy the Taleban and al-Qaeda forces."
The US has urged the Northern Alliance to occupy more ground before the onset of winter.
Secretary of State Colin Powell said last week that Washington wanted the Northern Alliance to take the strategic town of Mazar-e-Sharif, whose large airport could be used as a base for operations by US forces, but was still continuing discussion about whether a rebel march into Kabul would be "the best thing".
But as yet the opposition has not launched its own attack against Kabul and Mazar-e-Sharif.
During a Pentagon briefing on Monday, Mr Rumsfeld said the US was working with both the opposition Northern Alliance and tribes in southern Afghanistan to strengthen opposition to the Taleban.
The Chairman of the Joint Chiefs of Staff, Richard Myers, told reporters that in the past two days, US operations had placed a greater emphasis on hitting Taleban forces in the field rather than fixed infrastructure.
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