Baghdad, Iraq CNN  — 

Shoppers throng the open-air markets in central Baghdad, rummaging through stalls packed with fresh produce and spices.

Just hours before, Iran had attacked US positions in Iraq.

After years of proxy war between the US and Iran, this was a rare act of direct confrontation, but many Iraqis shrug it off.

“Unfortunately, we are students of war,” said Nihad Issam, a mother-of-two.

After decades of enduring cycles of violence, Iraqis are hardened to conflict. They say they are used to being stuck between global and regional powerhouses, and to paying the price for other countries’ wars.

Mohammed Hammed, 30, grills fish on a sidewalk in central Baghdad. He says the Iranian strike on Wednesday was "absolutely wrong."

“That was false,” said one Iraqi Christian man, sporting a cowboy moustache and a red beret, who asked not to be named for security reasons.

“This is a game between the US and other countries behind the curtains,” he told CNN. “The educated people in this country know what’s going on.”

Many Iraqis say they have little vested interest in Iran and the US’ latest tit-for-tat.

“They’re each thinking about their own interests,” said Amir Jamal, 40, who sells pickled vegetables on the sidewalk in central Baghdad. “I think our relationships [with the two countries] should be based on mutual interests. I don’t want either of them to control Iraqis anymore.”

The US and Iran have been jockeying for political dominance over Iraq since the US-led invasion in 2003.

Iran, which has backed Shia armed forces in the country’s civil war, eventually established a powerful foothold in the country.

Anti-government protesters whose demonstrations have swept across Iraq since October have spoken out against Iran’s influence, but Tehran still enjoys broad support in the country.

This was on display when large crowds of Iraqis came out onto the streets for the funerals of the Iraqis and Iranians killed in the US attack targeting General Qasem Soleimani.

“For every action there is a reaction,” said Jamal, reflecting on Iran’s retaliatory attack on US positions in Iraq on Wednesday. “I wasn’t surprised at all.”

"We want this war [between the US and Iran] to happen outside Iraq. We've had enough," says Amir Jamal.

The US killed Soleimani – Iran’s most powerful military commander – and Iraqi paramilitary leader Abu Mahdi al-Muhandis in an airstrike at Baghdad airport last Friday.

The killings sent shockwaves through the region, raising the specter of a wide-scale war in the region. A cautious calm hung over Baghdad. Even Iraq’s anti-Iran protesters condemned the attack, for breaching the country’s sovereignty.

Iraq’s government scrambled to push for legislation to expel US troops from the country. Caretaker Prime Minister Adel Abdul Mahdi said it would be Iraq’s only “way out” of the escalating Iran-US war.

Parliament voted unanimously in favor of instructing the US to withdraw its roughly 5,000 troops, but the lawmakers attending the session were predominantly Shia – most Sunni and all Kurdish MPs sat out the vote.

And across Baghdad, many Iraqis fear that a US withdrawal would make way for greater Iranian dominance in the country.

“The attack last night was absolutely wrong. It shouldn’t have happened,” said Mohammed Hameed, 30, on Wednesday, as he grilled fish over charcoal on the sidewalk. “Our interests are with America and not Iran.”

Hours after the Iranian strike, it was business as usual at central Baghdad's open marketplace.

US President Donald Trump has threatened to impose sanctions on Iraq if it expels US troops from the country. Iraq buckled under crippling sanctions for most of the 1990s, following former President Saddam Hussein’s invasion of Kuwait.

The prospect of returning to that era, which Iraqis refer to as “the days of the siege,” is too much for some to bear.

“The Americans should stay,” said Hameed. “I’m worried that if the Americans leave, we’ll have sanctions again.”

People in Baghdad are divided over whether US troops should stay or go.

The debate sparks screaming matches, and pro-American Iraqis are sometimes are accused of being “traitors,” but differences are, for the most part, dealt with peacefully.

Memories of civil conflict are all-too-fresh in people’s minds.

“We want this war [between the US and Iran] to happen outside Iraq. We’ve had enough,” said Jamal. “We have our differences, but we are aware that we are Iraqi nationals. Without this awareness, we head towards destruction.”