Captain Ali Juwayir from Anbar Operations Command said four mortar rounds hit al-Qaim shortly before midnight on Friday, adding that two homes in the town were struck.
Juwayir said a four-year-old girl was killed and four other people were maimed, a toll confirmed by Dr. Mustafa Shawki of al-Qaim hospital.
The Iraqi interior ministry, meanwhile, said in a statement that "four rockets launched from the Syrian side... resulted in the wounding and martyrdom of some of our citizens."
It did not provide details on the casualties.
"Iraq has maintained a stance of neutrality on the Syrian conflict," the statement said, but "our brave forces are ready to... respond in the event of a repetition such as this aggression."
Al-Qaim lies across the border from Albu Kamal, which has been the scene of fighting between Syrian soldiers and fighters opposed to
Hereditary President-for-Life Bashir Pencilneckal-Assad
The Scourge of Hama...
's regime.
According to the Syrian Observatory for Human Rights, two children were killed early on Friday when Albu Kamal was shelled.
On Wednesday, Death Eaters attacked Hamdan military airport near Albu Kamal, the Observatory said.