Protests demanding an overhaul of the political system have rocked Baghdad and the Shiite-majority south for weeks -- the crowds unmoved by government pledges of reform and undeterred by the deaths of more than 300 demonstrators.

Washington and the United Nations have called on the government to respond seriously to the protests, with the world body's representative Jeanine Hennis-Plasschaert saying the country's authorities must "step up to the plate and make things happen".

"They are elected by the people, they are accountable to them," the head of the UN's Iraq mission (UNAMI) told AFP in an exclusive interview.

US Secretary of State Mike Pompeo, for his part, has said he told Iraqi Prime Minister Adel Abdel Mahdi that he "deplored the death toll" and to address the popular movement's "legitimate grievances".

The protests had slowed for a few days following a deadly crackdown by security forces in Baghdad and major southern cities but flared again Wednesday with demonstrations by striking students and teachers.

"We're here to back the protesters and their legitimate demands, which include teachers' rights," said Aqeel Atshan, a professor on strike, in Baghdad's Tahrir (Liberation) Square, the epicentre of the protest movement.

In the southern port city of Basra, around 800 students returned to camp outside the provincial government headquarters, days after they had been pushed out by riot police.

Schools were also shut in the protest hotspots of Diwaniyah and Nasiriyah.

- Phased roadmap -

Protesters have felt emboldened since the country's top Shiite religious authority Grand Ayatollah Ali Sistani said they "cannot go home without sufficient reforms".

"Students, boys and girls alike, are all here for a sit-in," another demonstrator in Tahrir told AFP.

"If Sistani gave the orders for mass civil disobedience, everything would close -- the government, the oil companies, everything. That's how we'll have a solution."

The UN has put forward a phased roadmap, backed by Sistani, calling for an immediate end to violence, electoral reform and anti-graft measures within two weeks.

Hennis-Plasschaert, the UN envoy, discussed the plan with lawmakers during a parliamentary session on Wednesday afternoon.

"Now is the time to act, otherwise any momentum will be lost -- lost at a time when many, many Iraqis demand concrete results," she told them on the sidelines of the parliamentary meeting.

At the session's opening, speaker of parliament Mohammed al-Halbussi pledged to work on laws to respond to protesters' demands including electoral reform.

Parliament has received a draft law for electoral reform but has yet to discuss it.

Lawmakers also set dates to interrogate two ministers, which could indicate the first steps of a cabinet reshuffle announced by Abdel Mahdi.

Oil-rich Iraq is ranked the 12th most corrupt country in the world by Transparency International, and youth unemployment stands at 25 percent.

Demonstrations erupted on October 1 in fury over a lack of jobs and corruption, initially fracturing the ruling class.

Populist cleric Moqtada Sadr then called on the government to resign and President Barham Saleh suggested early elections, while other factions stood by Abdel Mahdi.

- Sadr, Saleh change tune -

But after a series of meetings led by Iran's influential Major General Qassem Soleimani, a consensus emerged at the weekend over the government remaining intact and both Saleh and Sadr appear to have changed their tunes.

Sadr, who is reported to be in Iran, took to Twitter on Wednesday to call on parliament to enact reforms and for "a general strike, even for one day," but did not demand the premier step down.

Saleh, too, appears to have dropped the idea of early elections.

The agreement brokered by Soleimani appeared to have paved the way for a crackdown on demonstrations last weekend that sent the death toll amid the unrest to well over 300.

Iraq has faced growing criticism over its response to rallies, with rights defenders accusing authorities of shooting live rounds at protesters and curtailing freedom of expression with an internet blackout and mass arrests.

Also on Wednesday, the president of autonomous Iraqi Kurdistan, Nechirvan Barzani, was in Baghdad to meet with the premier, president and speaker of parliament.

Barzani and Abdel Mahdi are believed to have good personal ties, and the Iraqi Kurdish authorities have backed the current government.

But they have worried that any amendments to Iraq's 2005 constitution as part of a reform process could infringe on Kurdish rights.