An SAS unit was reportedly involved in a skirmish with Taleban soldiers on the outskirts of the Afghan capital, Kabul.
A Ministry of Defence spokesman in Wellington would not comment on any SAS involvement in Afghanistan, but said the unit had troops attached to British units regularly.
Mr Goff said New Zealand's formal offer of help yesterday was "hugely appreciated" in Washington.
Measures included intelligence, the immediate strengthening of laws targeting terrorist activities, and the use of the special forces troops.
New Zealand has about 100 SAS troops, based at the Hobsonville air base.
They are constantly training in covert operations, the use of specialised weaponry, observation equipment and communications gear.
About 40 members were in the first wave to enter East Timor, 20 saw active service during the Gulf War, and one was caught up in the Sierra Leone conflict 18 months ago.
Military analysts believe such units will play a vital role in any attempt to capture bin Laden in rugged Afghanistan.
As the US-led military cordon converged on the country yesterday, the Taleban claimed to have recaptured much of the ground lost in the north and northwest in the past few days in fierce fighting with opposition forces.
Its leader, Mullah Mohammad Omar, called on Afghans who have fled Kabul to return to the city where protesters on Tuesday launched a frenzied attack on the abandoned American embassy.
Amid scenes of pandemonium, Taleban supporters set fire to cars and outbuildings, sending smoke billowing across the city.
Several men used hammers and crowbars to remove the US Government emblem above the entrance.
In another sign of defiance, the Taleban said the trial of eight foreign aid workers - including two Australians, two Americans and four Germans - charged with preaching Christianity would resume tomorrow.
Omar said 300,000 Afghans had signed up to resist any US-led invasion.
But relief agencies say up to one million Afghans are on the move, and thousands are fleeing to borders with Pakistan, Iran, Tajikistan and Turkmenistan.
The United Nations has launched the biggest appeal in its history, seeking $500 million to cope with the refugee crisis.
Aid workers tried to restart an emergency grain distribution programme in the northeast after the Taleban's weekend shutdown of the UN aid communications network and seizure of food supplies.
The increasingly paranoid regime has threatened to execute aid workers using radios and satellite communications equipment, fearing troop movement details could be passed to the West.
As dozens queued in New York for death certificates for the thousands killed in the World Trade Center, investigators probing the attacks made further arrests of alleged terrorists with possible links to bin Laden in Britain and Spain.
In the past week, investigators have revealed planned suicide strikes on the American embassy in Paris, the US consulate in Marseille, Nato buildings in Brussels and the European Parliament in Strasbourg.
In Brussels, US Deputy Defence Secretary Paul Wolfowitz met Nato defence ministers.
But hopes that Iran might be drawn into the alliance were scuttled by Iranian supreme leader Ayatollah Ali Khamenei, who said the US was not "sincere enough" to lead an international move against terrorism.
Map: Opposing forces in the war against terror
Afghanistan facts and links
Full coverage: Terror in America
