The Shia-led Iraqi government issued a carefully-worded statement on Friday, condemning the Khan Sheikhun attack - a first in the six-year Syrian conflict.
"We strongly support any effort exerted by the international community to punish those who use these weapons," the Iraqi Ministry of Foreign Affairs said without naming Assad.
The statement called for an international investigation to identify the perpetrator and also warned against "rushed interventions", referring to US President Donald Trump's retaliatory attack on Shayrat airbase the same day.
Until now Iraq has maintained good relations with the Assad regime, which is strongly backed by Baghdad's close ally Iran.
An Iraqi minister told The New Arab on Monday that the Trump administration has begun to pressure Prime Minister Haider al-Abadi to change his position on Syria and other issues in which "Baghdad has been influenced by Iran".
Abadi received phone calls from Trump, Vice President Mike Pence and US Secretary of State Rex Tillerson before his meeting with Trump's top aide and son-in-law Jared Kushner, the minister, who spoke on the condition of anonymity, said.
"This balancing act Iraqi authorities are maintaining between its alliances with the US and Iran will not last long. The time of free handouts from the US has ended," the minister added.
Influential Iraqi cleric Moqtada Sadr on Saturday called on Assad to step down, also calling on Washington and Moscow to stop intervening in the conflict.
"I would consider it fair for Assad to resign and leave power, allowing the dear people of Syria to avoid the scourge of war and terrorist oppression," he said in a statement.
Sadr's spokesman Jafaar al-Musawi told The New Arab that the cleric's message on Assad was "obvious".
"His eminence has always supported people's right to self-determination. If a leader sheds the blood of his own people he must step down even if he is the legitimately elected ruler," Musawi said.
Several Iraqi Shia militias, some of them directly supported by Iran, are helping Assad's camp by sending fighting units across the border.
According to The New Arab's Iraq correspondent Othman al-Mukhtar, dozens of militiamen loyal to Sadr have recently withdrawn from Syria's East Ghouta region.