The former king has said he wants to be of service
The alliance's political representatives are in Rome for talks with the exiled former king of Afghanistan, whose authority is being sought for proposed new governing bodies.
In Kabul, there were signs that normal life was resuming and militant foreign supporters of the Taleban were again making their presence felt.
The scattered pockets of anti-Taleban fighters are pinning their hopes on possible US strikes against their enemy.
According to the Tajik news agency Asia-Plus, the coalition has conceded losing a key district in the north to the Taleban.
A Northern Alliance diplomat based in Russia, Mohammad Saled Registani, was quoted as saying that anti-Taleban forces had briefly captured Zari District, 90 km (55 miles) west of Mazar-e Sharif, only to see their enemies retake it.
But, he added, the Northern Alliance had taken territory in the provinces of Badghis, Balkh and Samangan.
Russian and Tajik news agencies say at least 100 Taleban fighters were killed and hundreds captured in the fighting.
The same sources said the Northern Alliance had lost 35 of its fighters, including a commander close to General Abdorrashid Dostum.
Political moves
Deposed Afghan President Burhanaddin Rabbani has called on the West to help the Northern Alliance, calling it the "frontline in the war against terrorism".
The Taleban wrested power from Mr Rabbani in 1996, but most of the international community still recognises him as the country's legitimate leader.
In Rome, Northern Alliance representatives are due to meet the former King, Zahir Shah, on Sunday or Monday.
His spokesman, Zalmai Rassul, told the French news agency AFP that there were plans to establish a supreme council and a military council under the aegis of the 86-year-old exile.
He did not say if Zahir Shah had accepted the role.
"The composition of these two authorities will be decided in the next few days," he said.
Calm in Kabul
Life in the Afghan capital Kabul appears to be returning to normal after initial panic caused by fears of a US attack, the BBC's Afghanistan correspondent Kate Clark reports.
Residents speaking to the BBC by telephone said some people who had fled the city had now returned.
Owners of jewellery shops, for example, had brought their valuables back out of hiding and there were more people on the streets.
The ruling Taleban have ordered their feared religious police not to search people's houses, saying thieves had tricked their way into homes posing as policemen.
They have now been put on security duties, rather than dealing with moral crimes like making sure men's beards are untrimmed, or that they go to the mosque for prayers.
Those interviewed added that the Taleban's foreign Muslim allies - the Arab and Pakistani militants who fled Kabul in fear of an American attack - were once again a visible presence.
People said they felt safer because there had been no swift response to the 11 September attacks on New York and Washington, nor real movement towards Kabul from the Northern Alliance.
They also said that radio statements by the former king had also buoyed their hopes of a peaceful solution to the crisis.