Washington (CNN) The US announced sanctions Friday on the Iraqi leaders of three Iran-backed militias for killing dozens of innocent civilians who were protesting economic conditions and foreign interference in their country.

The State Department's senior official on Middle East affairs condemned Iran's interference in Iraqi affairs as he announced the sanctions. Assistant Secretary of State David Schenker also decried what he described as Tehran's increasing aggression in response to the Trump administration's maximum pressure campaign.

"Iraqis have played a step and bloody price" because of the Iranian regime's involvement in the country, Schenker said.

The Treasury Department designated Qais al-Khazali, Laith al-Khazali, and Husayn Falih 'Aziz al-Lami for their involvement in serious human rights abuses and a fourth person, Iraqi millionaire businessman Khamis Farhan al-Khanjar al-Issawi, for bribing government officials and engaging in corruption at the expense of the Iraqi people.

Exporting repression

Some 432 people have been killed since the start of anti-government demonstrations in Iraq on October 1, according to a source with the Independent High Commission for Human Rights of Iraq. Another 19,136 people have been injured in the demonstrations, the Commission has said.

It's clear to the US and to the region that "the theocracy's top export is corruption and repression," Schenker said of Iran.

For several weeks now, anti-government protesters in Iraq have been protesting endemic corruption, high unemployment, inadequate public services and Iran's interference in the country. They blame Iran for being complicit in the Iraqi government's failures and now its crackdown.

Schenker noted that Qassem Suleimani, leader of Iran's elite Quds Force, has recently been in Iraq in part "to determine the next political leader of Iraq."

"It is not normal," Schenker said. "This is unorthodox ... a huge violation of Iraqi sovereignty."

An Iraqi source told CNN the sanctions were expected, as the US had been signaling that they were coming. But this source said that the practical impact is "negligible," given that the designated Iraqis aren't thought to have any assets in the US.

Schenker acknowledged that the designations are "first and foremost" symbolic but said the US will be going after economic assets where they can and that more designations will be coming. "We are not done. This is an ongoing process," Schenker said, adding that anyone in violation of human rights inside or outside of the government is at risk of being sanctioned.

"We are holding these people to account," Schenker said.

He also noted that Iran-backed militias are now shelling Iraqi bases with American and anti-ISIS forces, saying it is "something of great concern." He said that Iran has taken aggressive action in the past when it feels under pressure and said that in the past six to eight months, Tehran has become more aggressive

When asked about the death toll of Iranians who have been killed amid the ongoing protests in Iran, Schenker gave an estimate of the low hundreds. He said that he did not know if the US had verified a number yet.

His statement comes the day after another senior State Department official, Brian Hook, briefed reporters and said that the US estimates that 1,000 Iranians have been killed in the protests there, a figure that is far higher than reports from rights groups, which put deaths among protestors in Iran around 200 people.