Military bases hosting USA troops have been subject to volleys of rocket and mortar attacks in recent months that have mostly wounded Iraqi forces, but also killed one American contractor last month.
Secretary of State Mike Pompeo alleged Monday that Iraqi leaders have told him privately they support the USA troop presence, despite public appeals for them to leave.
CNN has published a video of the aftermath of last week's missile attack on a United States military base in Iraq, which was staged by Iran in response to the assassination of high-ranking Iranian General Qasem Soleimani. The incident was decried by Secretary of State Mike Pompeo hours later.
"These continued violations of Iraq's sovereignty by groups not loyal to the Iraqi government must end", he added. Four people, including two officers, were injured. USA officials have insisted Soleimani was plotting attacks on US facilities.
Both elements saw their missions suspended last week, with orders for the troops to hunker down on military bases or, in some cases, relocated to Kuwait, over fears Iran or its proxies would retaliate for the USA having killed Iranian Maj.
The attack was ordered by US President Donald Trump who described it as a preemptive and defensive strike aimed at destroying "the terrorist number one anywhere in the world".
On Sunday, Esper and national security adviser, Robert O'Brien, said on nationally televised TV that Iran may have struck more than just the U.S. Embassy in Iraq.
Rocket attacks against Baghdad's high-security Green Zone, where the USA and other embassies are based alongside global troops, are still taking place.