Police forces fired into the air to disperse around 500 protesters, who had been throwing rocks in Basra, on Sunday.
Meanwhile, brief clashes erupted in Baghdad between security forces and a few hundred young people who returned to Tahrir Square on Sunday for a flash protest.
On Saturday, security forces cleared out sit-in tents from Tahrir Square and opened the previously blocked-off roads.
The government said al-Jamhuriya Bridge, which connects the square with the heavily fortified Green Zone housing some of the main government offices and foreign diplomatic missions, had been opened for the first time since it had been shut at the beginning of protests in October last year.
Some of the demonstrators had welcomed the clearing of the camp, saying it had been infiltrated by elements attempting to undermine the protests with violence and disruption.
A protest also took place in Nasiriyah against unemployment and poor public services. The demonstrators torched tires on a main highway in the southern city.
Dozens of people also staged a protest in the town of Kut, and demanded justice for those killed in demonstrations over the past year.
A similar demonstration took place in the city of Hilla.
The first anniversary of anti-government demonstrations that erupted in October 2019 was marked last week by hundreds rather than an anticipated thousands taking to the streets of Baghdad
Protests erupted in Iraq in October last year over unemployment and a lack of basic services, with demonstrators calling for economic reforms and a meaningful fight against corruption in state institutions.
Reports say about 600 people were killed and 30,000 injured as the anti-government rallies took a violent turn.
The protests led to the resignation of prime minister Adil Abdul-Mahdi, who was replaced by Mustafa al-Kadhimi in May following months of political deadlock.
In a televised address on October 24, Kadhimi vowed to hold early and fair elections, a demand of many protesters, and called on security forces not to fire at demonstrators, but also called on protesters to “respect the uniform”.