Many Iraqi Kurds long for Kirkuk as the eventual capital of their own state.
Last year the oil-rich city seemed close to becoming a permanent center of Kurdish power.
Now, hopes for a Kurdish Kirkuk have faded.
An Iraqi national election on Saturday is expected to weaken the main Kurdish parties there.
The peshmerga, Iraqi military and Shi’ite Muslim militias defeated Islamic State in 2017.
Within weeks, Iraqi government forces advanced on Kirkuk and captured it quickly.