NBC's Richard Engel reports for TODAY that fighting may intensify once soldiers reach built-up areas inside the city.
"[The] failure of the international community to protect civilians and halt this bloodshed should haunt every one of us," Zeid Ra'ad al-Hussein said.
Local Kurdish television channel Rudaw aired footage showing black smoke rising over the city as extended bursts of automatic gunfire rang out.
Late autumn storms drenched central Pennsylvania, knocking out power and forcing drivers to seek cover.
Militants came under fire from Kurdish forces after seizing a building in the northern Iraqi city.