"Iraq has high-level contacts (with parties of dispute), and we are going to push for calm between Washington and Tehran. But it's not a mediation," Xinhua news agency quoted Abdul Mahdi as saying at a press conference.
"The US and Iranian officials have assured us that they have no desire in fighting a war," he said.
On May 15, the US State Department ordered the non-emergency US employees at the embassy in Baghdad and the consulate in Erbil to leave Iraq, according to a US embassy statement.
Earlier, the US military said the US forces were on high alert in Iraq and Syria over fears of "imminent threats" from Iran-backed forces in the region.
Earlier in the day, Iranian President Hassan Rouhani ruled out the possibility of negotiations with the US.
In recent weeks, the US has ended waivers for Iranian oil imports, announced sanctions on Tehran's non-proliferation activity associated with the 2015 nuclear deal and sent a Navy strike group and bomber into the Persian Gulf as US officials leaked reports that claimed a heightened threat from the country, CNN reported.
In response, Iran announced it would stop complying with the nuclear deal.
On Monday, an Iranian energy official announced the country had increased its uranium enrichment four-fold and had informed the International Atomic Energy Agency.
( With inputs from IANS )