Bodies of eight militants were delivered to Qaim hospital morgue, Reuters said.
A lawmaker from Anbar, Ahmed al-Salmani, also said 55 civilians were killed.
Another lawmaker, Mohammed Karbouli, told Reuters that 60 people had been killed, including some of his relatives.
In a statement, Speaker Salim al-Juburi condemned the airstrike "that targeted a market area for civilians and resulted in the death and injury of dozens of them."
Al-Juburi said he "holds the government responsible for such mistakes" and demanded an immediate probe.
If confirmed, the incident would be one of the worst cases of civilians being killed in strikes in Iraq since 2014, the start of the air campaign against the Islamic State.
While speaking to AFP, a spokesman for the provincial council of Anbar alleged that the strike was carried out by an Iraqi aircraft in the afternoon.
"The strike hit a market at peak hour, there were retirees queueing up pick up their pension, people collecting salaries and social security payments," Eid Ammash said.
"Entire families were killed," Ammash said.
Maath al-Jughaifi, a tribal leader from the nearest city of Haditha, told AFP that "between 70 people and 80 people were killed" in Al-Qaim but claimed the strike was carried out by the US-led coalition.
An unverified footage released by Amaq, an IS-affiliated propaganda website, shows the aftermath of the strike and claimed 120 people were killed.