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Iraqi Prime Minister Adel Abdel Mahdi says he accepted the "just demands" of the protesters after three days of calm.
In a rare broadcast, Prime Minister Mahdi spoke of reconciliation as protesters demanded resignation.
The House of Representatives said they would respond to their concerns, but warned there was no "magical solution" to Iraq.
At least 20 people were insecure as the anger of unemployment and corruption disappeared.
Baghdad and other cities in southern Iraq were imposed curfews, but thousands ignored them and lived in by security forces.
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What did Mahdi PM say?
Mr. Mahdi asked lawmakers to support him and promised to pass a new bill that would give basic income to poor families.
Mr. Mahdi said, "I am confident once again that your voice was heard before the protests started."
But he added that it would take time to make a difference.
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Getty images
PM Mahdi has so far preferred to communicate with written statements
The protests, which seem to lack organized leadership, are the biggest protests since Prime Minister Mahdi became Prime Minister a year ago.
The United Nations and the United States expressed concern about violence and urged Iraqi authorities to exercise arrest.
On Thursday, Amnesty International urged the Baghdad government to send security forces immediately.
What happened on thursday?
Dawn began an indefinite curfew in Baghdad that applies to everyone except those traveling to and from the capital airport. Ambulances and religious pilgrims were also excluded.
Security forces blocked major roads and bridges. Internet access has also been restricted, making it more difficult to organize protests on social media.
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Reuters
Protesters headed into the streets of Baghdad despite a ban on Thursday.
However, thousands of demonstrators gathered in Tahrir Square, the focal point of recent anxiety, urging the riot police to tear and fire and disperse gas and guns.
Ali, a 22-year-old unemployed university graduate, told AFP, "We will continue until the government collapses."
"While government officials have millions, I have only 250 lire ($ 0.20; £ 0.16) in my pocket."
More in Iraq:
Violence is concentrated in Baghdad and the Shiite Muslims in the south. Most of northern Kurd and many Sunni regions in the west are calm.
Police and hospital sources Thursday said Reuters had killed demonstrators in the capital, the southern cities of Amara, Diwaniya, Hilla and Na Siriya. Hundreds were injured.
On Wednesday night, an explosion took place in the fortified Green Zone of Baghdad, where there were government agencies and foreign embassies.
The US-led coalition, which is fighting Iraqi Islamic state groups, has not hit the facility and says Iraqi security forces are investigating the explosion.
What caused anxiety?
The protests seem to be the result of voluntary frustration with Iraq's high youth unemployment rate, serious public services and chronic corruption.
Baghdad journalist Simona Foltyn told the BBC's World Update Program: "Elderly people with all broadcast complaints that have accumulated over the years."
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"They all denied political involvement. They actually felt extreme renunciation and disappointment in the political system here."
She added: "Everyone who protests seems to be united in one thing. They want a better life. They want service, they want a job, they want a standard of living."
Last year, the southern Iraqi city of Basra suffered weeks of protests against unsafe drinking water, power shortages, unemployment and corruption. Government officials, including the main local council building, got off.
What is the economic situation in Iraq?
According to the World Bank, Iraq has the fourth largest oil reserve, but 22.5{7be40b84a6a43fc4fae13304fce9a2695859798abfc41afd127b9f8b21c5f9c5} of the 40 million people live on less than $ 1.90 a day (1.53 pounds) per day in 2014. One in six households has experienced some form of food insecurity.
Last year's unemployment rate was 7.9{7be40b84a6a43fc4fae13304fce9a2695859798abfc41afd127b9f8b21c5f9c5}, but doubled among young people. And nearly 17{7be40b84a6a43fc4fae13304fce9a2695859798abfc41afd127b9f8b21c5f9c5} of the economically active population is unemployed.
Iraqi Unemployment
Modeled ILO Estimates,{7be40b84a6a43fc4fae13304fce9a2695859798abfc41afd127b9f8b21c5f9c5}
The country is also struggling to recover in the cruel war with a group of Islamic nations that dominated the large pastures of north and west in 2014.
The Iraqi government and the World Bank estimated that $ 88 billion (£ 71 billion) was needed to fund short- and medium-term reconstructions last year.
According to the United Nations, over one million people are still migrating internally and 6.7 million people need humanitarian assistance, the UN said. Insufficient basic services, severe living conditions in areas affected by many conflicts.