Three Katyusha rockets fell on Tuesday inside Baghdad's Green Zone, which houses government buildings and foreign missions, Iraqi police sources told Reuters.

The three rockets were launched from Zafaraniyah district outside Baghdad, the sources said, adding that two rockets landed near the United States embassy

Sirens could be heard across the zone immediately after the rockets made impact.

The US has blamed Iran-backed paramilitary groups for a spate of similar attacks in recent months on the Green Zone, but there has never been a claim of responsibility.

Tensions in Iraq have risen since the US assassinated Qassem Soleimani, an Iranian military commander, in Baghdad on January 3.

That killing came amid widespread anti-Iraq government demonstrations, which are continuing.

Five protesters were killed on Monday in three Iraqi cities as demonstrators across the country ramped up pressure on the government to implement long-awaited reforms.

The United Nations envoy to Iraq urged Iraqi political elites to resume pushing for reforms and for protests to remain peaceful.

"Any steps taken so far to address the people's concerns will remain hollow if they are not completed," said envoy Jeanine Hennis-Plasschaert in a statement issued by the UN. "Violent suppression of peaceful protesters is intolerable and must be avoided at all costs."