Mr Hadi and Gulf allies have accused Iran of arming the Houthis, which Tehran strongly denies.
Iranian foreign minister Mohammad Javad Zarif said on Tuesday Tehran was proposing “a ceasefire followed by all-inclusive Yemeni dialogue that is facilitated by others, leading to the formation of a government in Yemen that represents a broadly based community”.
Mr Hadi, who has taken refuge in Riyadh, is considered the legitimate head of state by the United Nations, and Saudi Arabia launched the air strikes at his request.
Saudi warplanes pounded rebel positions again overnight in the battleground southern city of Aden, where Mr Hadi had taken refuge before fleeing the country last month as the Houthis approached, residents said.
Violent clashes between rival forces also rocked several central districts, residents said.
Mr Zeid said attacks on hospitals and on civilians unconnected to the fighting were war crimes.
“Any suspected breach of international law must be urgently investigated with a view to ensuring victims’ right to justice and redress and to ensure that such incidents do not recur,” he said.