The alliance has also asked the United Nations to send "teams" to the Afghan government to help the peace process, said the foreign minister, Abdullah, who goes by one name.
Abdullah spoke at a news conference in the capital hours after the Taliban abandoned the city and alliance fighters moved in. He insisted the alliance was "absolutely" committed to forming a government with other factions and ethnic groups - except the Taliban.
"We invite all Afghan groups to participate, to come to Kabul and to start negotiations and to speed up the negotiations about the future of Afghanistan," he said.
"We have also invited the United Nations to send their teams in Kabul in order to help us in the peace process," he said.
Abdullah defended the alliance decision to send troops into Kabul, something the United States had requested it refrain from doing.
He said alliance troops had planned to stop at the capital's edge but was obliged to enter because unruly elements were causing trouble.
"There was no option for us but to send or security forces into Kabul," he said.
The alliance defense minister, Mohammed Fahim, was leading a military security council to administer Kabul and maintain security, Abdullah said. The alliance's nominal leader, Burhanuddin Rabbani was in the northern city of Faizabad and would come to Kabul "when necessary," he said.
The alliance has deployed 3,000 security troops around the city to ensure order and guard international aid organizations, Yunis Qanoni, the alliance interior minister, said.
Qanoni said troops on the edge of Kabul would remain there until a "shura" council, gathering representatives from the country's ethnic groups, can be convened to decide on the government.
The alliance is made up of ethnic minorities, particularly Tajiks and Uzbeks. The United States and its allies insist that Pashtuns, the country's largest ethnic group and the backbone of the Taliban, must be included in any post-Taliban government.
Abdullah denied reports that opposition fighters had massacred Taliban in areas the alliance captured in its five-day sweep that brought the entire north under its control.
The United Nations reported Tuesday that more than 100 Taliban fighters hiding in a school were executed in the northern city of Mazar-e-Sharif on Saturday.
Elsewhere in Afghanistan, he said the situation in the southern city of Kandahar - the headquarters of the Taliban movement - was "chaotic" and that there was a popular uprising against Taliban rule in the eastern city of Jalalabad.