"We emphasize that there are no combat forces from any country on the Iraqi territories in the first place so that we can discuss [whether] they can stay or not", said a statement from Prime Minister Haidar al-Abadi's office Friday morning.
Any forces who remained would continue to be designated as advisers for the same reason, the Iraqi government official said.
During a congressional hearing in March, Joseph Votel, head of U.S. Central Command, said the fight for Mosul had left 774 Iraqi security forces dead and 4,600 wounded.
The new push would help the special forces of the Counter-Terrorism Service (CTS) and the interior ministry federal police, who are making slow progress in the southern part of Mosul's western side due to the stiff resistance of the extremist militants at the densely-populated areas of the old city center, where roughly 400,000 residents are believed to still be trapped under IS rule.
Iraqi security forces also launched an operation against Daesh positions in the Zanjili neighborhood of western Mosul, killing a senior militant commander identified as Hassan Jomeh Hassan.
The official said "several thousand. similar to what we have now, maybe a little more", troops would stay in the country, but added that discussions were in early stages and "nothing has been finalized".
A few days after the 82nd's deployment, the Trump administration announced that it would cease disclosing information about the scope and nature of future us troop deployments in both Iraq and Syria, citing operational security and "tactical surprise".
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USA forces were aware of their location and movements, he added, but did not interact with them in any way. That number dropped to 40,000 before complete troop withdrawal in 2011.
He said they will work to train Iraq's security forces to maintain "full readiness" for any "future security challenges".
Originally, the United States anti-IS campaign, which was launched in 2014 after Mosul fell to the militant group, was primarily focused on providing air support and military expertise.
During a visit to Iraq in February, Mattis and Lt. Gen. Stephen Townsend, the top US commander in Iraq, described an enduring partnership between the USA and Iraq. Iraq and Iran also share a religion, a long border and in some cases, national interests in the region.
The talks over a longer-term USA presence has greatly concerned Iran, which in turn is increasing support to some of Iraq's Shiite militia forces, said Jafar al-Husseini, a representative from Kataib Hezbollah, an Iraqi Shiite militia group with close ties to Iran.
After a territorial victory, Iraqi and US-led coalition officials have warned of the potential for IS to carry out insurgent attacks in government held territory.