The U.S. -led coalition fighting Islamic State militants said on Friday it had confirmed another 61 likely civilian deaths caused by its strikes in Iraq and Syria, raising to 685 the number of civilians it has acknowledged killing since the conflict began. It has offered a reward of up to $25m (£19.6m) for information leading to his capture or death.
"Do I believe he's alive?".
However, Townsend said: "I've seen no convincing evidence, intelligence, or open-source or other rumour or otherwise that he's dead ..."
"There are also some indicators in intelligence channels that he's still alive", said General Townsend.
In June, Russia said there was a "high probability" that Baghdadi had been killed a month earlier in a Russian airstrike on Raqqa, the terror group's de facto capital in northern Syria.
Townsend was speaking to reporters at the Pentagon from his headquarters in Baghdad.
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Assessing his 12 months in command of the US -led coalition, Townsend said more tough fighting remains but signs are positive.
The city had become the next target of the US-backed war on the jihadist group following the capture of Mosul, where it had declared its "caliphate" over parts of Iraq and Syria in 2014.
"We all saw what happened in 2011 when we parted ways completely", he said, referencing the pullout of USA troops under former President Barack Obama and Iraq's subsequent struggles.
In previous briefings, Townsend would not comment on Baghdadi's status.
"We're looking for him every day, I do not think he's dead", he said.
"A key result of that is that we don't get second-guessed a lot", he added. "This time, we surrounded Tal Afar and launched airstrikes against IS and managed to reduce the extremists' fighting capability by more than 90 percent", Brigadier General Yahya Rasool added.