On October 4, a US airstrike on a Doctors Without Borders hospital killed 22 civilians. The US military on Monday said the strike was launched after Afghan forces taking gunfire called for air support.
UN Secretary-General Ban Ki-moon has called for an "impartial" investigation, but did not say it should be carried out by the UN.
"It's still early days, I think we're waiting to see what comes out of the official U.S. and NATO and possibly Afghan investigations," he said. "I think what we're looking for is a credible and transparent investigation."
Doctors Without Borders and Zeid Ra'ad Al Hussein, the UN human rights chief have said the incident could be a war crime.
US Defense Secretary Ash Carter has promised a full investigation into the airstrike.
Under international law, the bombing would only be a war crime if it was proved that the hospital was attacked intentionally, legal experts told Reuters.
A UN investigation is unlikely at this point because the United States is viewed as capable of carrying out a credible investigation and because the incident is not viewed as part of a systematic campaign targeting civilians, diplomatic sources said. If doubts arose over the credibility of the US or NATO investigations, there might be calls for a UN probe, Reuters reported.
Doctors Without Borders, which said they had given the hospital coordinates to US and Afghan forces, has called for a "full transparent independent investigation."
Zeid Ra'ad al-Hussein on Saturday said that "if established as deliberate in a court of law, an air strike on a hospital may amount to a war crime."