The leader of the so-called Islamic State terror group, Abu Bakr al-Baghdadi, is still alive, according to the the US commander of forces fighting in Iraq.

Army Lieutenant General Stephen Townsend told reporters he had seen "some indicators in intelligence channels" that al-Baghdadi is alive, but gave no further details.

His claim contradicts Moscow's assertion that al-Baghdadi was killed in a Russian air strike.

Russian officials said in June there was a "high probability" that al-Baghdadi had been killed alongside other senior militants just outside Raqqa, the group's de facto capital in Syria.

Townsend was speaking to reporters at the Pentagon from his headquarters in Baghdad.

He said US forces are actively searching for al-Baghdadi, adding that if they find him they probably will kill him rather than capture him.