Six rockets landed on Sunday in northern Iraq's autonomous Kurdistan region, Kurdish counter-terrorism forces said, with "minor damage" at a key oil refinery, according to another security source.
"Six rockets fell near the Zab river in the Khabat district," the Kurdish forces said, without specifying the target.
The attack caused no casualties or damage, the forces said.
But other sources said two rockets hit part of the Kawergosk refinery north-west of the Kurdish capital Erbil, causing "minor material damage".
A fire broke out at the site but was "quickly contained", one of the sources said.
Responsibility for the attack was not immediately claimed.
The Kurdish counter-terrorism forces said the rockets were fired from the town of Bartella in neighbouring Nineveh province.
Nineveh is under the administration of the Iraqi government in Baghdad.
Its capital Mosul was once the stronghold of ISIS before it was retaken by pro-government forces in 2017.
In early April, three rockets landed at Kawergosk, with no casualties or damage reported.
The April rocket fire came less than a month after Iran's Islamic Revolutionary Guard Corps claimed responsibility for ballistic missile fire in Erbil on an "Israeli strategic centre".
Kurdish authorities have insisted that Israel has no sites in or near Erbil.