High Commissioner Zeid Ra'ad Al Hussein encouraged a full and straightforward examination concerning the assault.
Restorative philanthropy Medecins Sans Frontieres said no less than 12 of its staff and seven patients were executed.
US strengths were doing air strikes at the time.
No less than 37 individuals were genuinely harmed, 19 of them MSF staff.
"All signs as of now indicate the besieging being completed by global Coalition powers," MSF said.
The Nato collusion has conceded its powers may have hit the healing center.
US President Barack Obama communicated his "most profound sympathies" for the passings in a White House proclamation. Be that as it may, he said he would hold up until the US protection office had led its own particular examination before making an authoritative judgment on the occurrence.
UN High Commissioner Zeid prior said: "Universal and Afghan military organizers have a commitment to regard and secure regular citizens at all times, and restorative offices and staff are the object of an exceptional insurance.
"These commitments apply regardless of whose aviation based armed forces is included, and independent of the area."
MSF said that all gatherings to the contention, including Kabul and Washington, had been told the exact GPS co-ordinates of the clinic on numerous events, including on 29 September.
In an announcement, the philanthropy said all signs indicated the bombarding being done by global coalition strengths.
It reported that from 02:08 until 03:15 nearby time, the doctor's facility was hit by a progression of elevated bombarding strikes at around 15-minute interims.
The principle focal doctor's facility building - lodging the emergency unit, rooms, and physiotherapy ward - was over and again hit amid every aeronautical strike while encompassing structures were left generally untouched, it included.
"The bombs hit and afterward we heard the plane circle round," said Heman Nagarathnam, MSF head of projects in northern Afghanistan.
"There was an interruption, and after that more bombs hit. This happened over and over. When I made it out from the workplace, the fundamental doctor's facility building was overwhelmed on fire. Those individuals that could had moved rapidly to the building's two shelters to look for security."
MSF president Meinie Nicolai depicted the episode as "despicable and a grave infringement of global helpful law".
She included: "We request complete straightforwardness from coalition strengths. We can't acknowledge that this awful death toll will essentially be released as 'inadvertent blow-back'."
A representative for US strengths in Afghanistan, Col Brian Tribus, said: "US powers led an air strike in Kunduz city at 02:15 (nearby time)... against people undermining the power.
"The strike may have brought about inadvertent blow-back to an adjacent restorative office."
In an announcement, US Defense Secretary Ash Carter said: "While we are as yet attempting to focus precisely what happened, I need to extend my considerations and requests to God to everybody influenced.
"A full examination concerning the appalling occurrence is under path in co-appointment with the Afghan government."
Gen John Campbell, the authority of US powers in Afghanistan, later affirmed the air strike was "in the region" of the MSF office however was focusing on "radicals who were specifically terminating upon US administration individuals".
Afghan President Ashraf Ghani said the US-drove Nato power had offered sympathies over the episode.
Taliban dissent
The Afghan inside service said a gathering of 10 to 15 activists were covering up in the healing facility.
"They are executed, the terrorists' majority were slaughtered, yet we likewise lost specialists," service representative Sediq Sediqi said.
The Taliban precluded that any from claiming its warriors were there.
A Taliban explanation depicted the air strikes which hit the healing facility as "conscious", and completed by "the boorish American strengths".
MSF says that staff and patients discriminatingly harmed in the assault on the clinic have been exchanged to a doctor's facility in Pul-e Khumri, two hours' head out.
There has been extraordinary battling in Kunduz since Taliban contenders cleared into the northern city on Monday.
