BAGHDAD/WASHINGTON (Reuters) - The United States on Friday blacklisted three Iran-backed Iraqi paramilitary leaders over their alleged role in killings of anti-government protesters in Iraq and threatened future sanctions if violence against demonstrators continued.

FILE PHOTO: Iraqi Popular Mobilisation Forces (Hashid Shaabi) march during the funeral of members of Shi'ite group Asaib Ahl al-Haq, who were killed when protesters attacked the group's office during anti-government protests, in Baghdad, Iraq October 26, 2019. REUTERS/Thaier Al-Sudani

The sanctions announced on Friday are the latest U.S. targeting of Iraqi individuals or armed groups with close links to Tehran as Washington ramps up economic pressure to try to counter Iranian influence in the Middle East.

Washington would be ready to impose further sanctions on others over the killings of protesters if the violence did not stop, David Schenker, Assistant Secretary for Near Eastern Affairs, told reporters in a briefing.

“We are not done. This is an ongoing process,” he said.

The sanctions target Qais al-Khazali, leader of the Asaib Ahl al-Haq Iran-backed militia and his brother Laith al-Khazali, another leader of the group, according to a statement from the U.S. Treasury Department.

They also target Hussein Falih al-Lami, security chief for the Popular Mobilization Forces (PMF), Iraq’s state umbrella group of paramilitary factions, which is dominated by groups backed by Iran, including Asaib.

The Treasury Department said in its statement that groups led by the three paramilitary leaders “opened fire on peaceful protests, killing dozens of innocent civilians.” Reuters reported last month that Lami, known also as Abu Zainab al-Lami, had directed fighters to open fire on protesters.

Iraqi paramilitary groups deny any role in the deaths of protesters, who have demonstrated against the government for more than two months. Security forces have killed more than 400 mostly unarmed protesters, police and medics say.

On Friday, gunmen killed at least six people near Tahrir Square in central Baghdad, police and medics said.

The new sanctions also targeted Iraqi businessman Khamis al-Khanjar for alleged corruption, the statement said.

Schenker said the sanctions, which freeze any U.S. assets held by the leaders and prohibit Americans from doing business with them, are “first and foremost symbolic” but also have a financial impact.

Senior U.S. Treasury officials said the violent crackdown on protests was “causing even more political instability.”

“Iraqis have a fundamental right to a political process that is free from foreign malign influence and the corruption that both comes with it and fuels it,” one of the officials said.

They said the militia leaders had been involved in forced disappearances and abductions of activists.

Iran-backed armed groups and politicians have dominated Iraq’s state institutions since a U.S.-led invasion in 2003 that toppled dictator Saddam Hussein, plunged the country into years of civil war and destroyed infrastructure.

Iraqi protesters say the groups that dominate the government have kept people poor and jobless through corruption and failed to repair the country despite two years of relative calm after the defeat of Islamic State.

Iraqi Prime Minister Adel Abdul Mahdi said last week he would quit.

Asked whether sanctions were designed to distance the militia leaders from the process of forming a new government, one of the Treasury officials said: “The timing is quite deliberate... Iraq’s people are demanding a government that is free and clear of foreign interference.”

Tension between Washington and Tehran has ramped up as U.S. President Donald Trump’s administration blames Iran for a series of attacks on oil infrastructure in the Gulf and bases hosting U.S. troops in Iraq. Iran denies involvement in the attacks.

Iraqi paramilitaries have in turn accused the United States and Israel of attacks on their own installations.

James Jeffrey, the U.S. special envoy to the global coalition fighting Islamic State, arrived in Baghdad on Thursday to meet with officials and discuss the fight against the militant group in Iraq and Syria, the State Department said in a statement on Friday.