CAIRO — The United Nations’ human rights chief warned on Tuesday thatYemen was on the brink of collapse, as health officials in the southern port city of Aden described a medical system failing after weeks of urban warfare that had left scores dead and hospitals overflowing with bodies.

The warning from the human rights chief, Zeid Ra’ad al-Hussein, came as a Saudi-led military offensive against the Houthis, a militia group from northern Yemen that Saudi officials have accused of serving as a proxy force for Iran, threatened to burst into a broader conflict.

The Houthis, acknowledging their alliance with Iran but denying acting on its orders, have been able to extend their offensive despite intensifying airstrikes by Saudi warplanes across Yemen.