Supporters of an influential Iraqi Shiite cleric fired rocket-propelled grenades and machine guns into Iraq's Green Zone as security forces returned fire on Tuesday, seriously escalating a month-long political crisis gripping the nation.

The death toll rose to at least 30 people after two days of unrest, officials said.

Those backing cleric Muqtada al-Sadr, who resigned suddenly on Monday amid a political impasse, earlier stormed the Green Zone, once the stronghold of the US military that's now home to Iraqi government offices and foreign embassies.   At least one country evacuated its diplomatic personnel amid the chaos.

Iraq's government has been deadlocked since al-Sadr's party won the largest share of seats in October parliamentary elections but not enough to secure a majority government — unleashing months of infighting between different Shiite factions.

Al-Sadr refused to negotiate with his Iran-backed Shiite rivals, and his withdrawal on Monday has catapulted Iraq into political uncertainty and volatility with no clear path out.

The violence threatened to deepen the political crisis, though streets elsewhere in the country largely remained calm and the country's vital oil continued to flow. Iran closed off its borders to Iraq — a sign of Tehran's concern that the chaos could spread.

Live television footage showed supporters of al-Sadr firing both heavy machine guns and rocket-propelled grenades into the heavily fortified Green Zone through a section of pulled-down concrete walls. Bystanders, seemingly oblivious to the danger, filmed the gunfight with their mobile phones.

As al-Sadr's forces fired, a line of armoured tanks stood on the other side of the barriers that surround the Green Zone. Heavy black smoke at one point rose over the area, visible from kilometres (miles) away.  At least one wounded man was taken away in a three-wheel rickshaw, the Iraqi Foreign Ministry visible in the background. At least 30 people have been killed and over 400 wounded, two Iraqi medical officials said. The toll included both al-Sadr loyalists killed in protests the day before and clashes overnight.

Those figures are expected to rise, said the officials, who spoke on condition of anonymity because they weren't authorised to release the information to journalists.