A Northern Alliance envoy has expressed regret at "any ill treatment" of Afghans after Taliban forces fled Kabul.
He also underlined the opposition's commitment to building a broad-based government.
Mr Ravan Farhadi told the UN General Assembly opposition forces were left with no option but to deploy a limited number of police in the city after Taliban fighters left the Afghan capital on the verge of chaos and mayhem.
Mr Farhadi represents the deposed government of Mr Burhanuddin Rabbani, whose faction dominates the alliance that now controls Kabul and about half the country. Mr Rabbani was Afghanistan's president from 1992 until 1996, when the Taliban captured Kabul.
The opposition has no intention "to monopolise power," said Mr Farhadi in a bid to reassure diplomats at the annual assembly debate.
"It is our sincere hope that the people of Afghanistan will democratically decide in the near future what form of political system they desire," Mr Farhadi said. "All ethnic groups must be equally represented and given a voice".
Before his address, the UN Security Council voted to endorse a UN plan seeking to build a broad-based government that would represent all factions and ethnic groups in Afghanistan.
Mr Lakhdar Brahimi, the top UN envoy for Afghanistan, will try to convene a meeting of Afghan leaders to decide on the country's future.
AP