Abadi flew straight into the city from Brussels where he attended a NATO summit to discuss the Islamic State group and immediately held talks with officials, a statement said.
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Demonstrations have been ongoing over the past several days, with protesters in some cases setting tyres ablaze to block roads and trying to storm government installations.
The protests erupted on Sunday and security forces opened fire killing a protester, sparking further anger.
As well as unemployment, protesters are frustrated by rising living costs and a lack of basic services in the city, the capital of Basra province.
There were further protests on Friday morning and calls for a demonstration in the afternoon in front of the local provincial headquarters.
On Thursday Oil Minister Jabbar al Luaibi said protesters tried to break into an oil installation in the West Qurna oil field of Basra province.
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In a statement released by his office, Luaibi said the demonstrators failed to enter the area but had set fire to a gate and a security post.
Officially, 10.8% of Iraqis are jobless, while youth unemployment is twice as high in a country where 60% of the population are aged under 24.
Abadi has vowed to rebuild the economy, ravaged by years of conflict, but frustrations have been growing especially in the oil-rich south.
Iraq is the second biggest producer of crude in the OPEC oil cartel, with 153 billion barrels of proven reserves.
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