BAGHDAD — In a sign of a split in the coalition of Sunni Muslim forces supporting the Islamic State of Iraq and Syria, the militants clashed with an Iraqi Baathist faction allied with them, Iraqi security officials said on Saturday.

The clashes took place in western Kirkuk and the suburb of Hawija, a longtime stronghold of the Men of the Army of Naqshabandi, a group formed by former army officers from the Saddam Hussein regime who joined with the Islamic State of Iraq and Syria, or ISIS, in its drive through Iraq.

The security official, speaking on condition of anonymity in line with official policy, said militants from the two factions fought one another Friday night after ISIS tried to disarm the Naqshabandi. However, someone in Hawija who witnessed the clash said that the two factions fought over control of gasoline and oil tanker trucks brought by the Sunni militants from the refinery at Baiji, which they have been attacking for nearly a week now.

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In a separate development, President Vladimir V. Putin of Russia called Prime Minister Nuri Kamal al-Maliki of Iraq and offered Russia’s “full support for the Iraqi government’s efforts to liberate Iraqi territory from the terrorists’ hands as quickly as possible,” according to a statement issued Saturday by the Kremlin.