BAGHDAD/FALLUJA (Reuters) - U.S. and Iraqi officials said on Friday they could not confirm a report by an Iraqi TV channel that Islamic State leader Abu Bakr al-Baghdadi had been wounded in an air strike in northern Iraq.

A man purported to be the reclusive leader of the militant Islamic State Abu Bakr al-Baghdadi has made what would be his first public appearance at a mosque in the centre of Iraq's second city, Mosul, according to a video recording posted on the Internet on July 5, 2014, in this still image taken from video. REUTERS/Social Media Website via Reuters TV

A spokesman for the U.S.-led coalition fighting the radical Islamist militants, Colonel Chris Garver, said in an email that he had seen the reports but had “nothing to confirm this at this time”.

Brett McGurk, the U.S. envoy to the coalition, told a daily briefing at the White House in Washington that there was no reason to believe that Baghdadi was not alive “even though we haven’t heard of him since late last year.”

“We presume that he’s still alive,” he added. “It’s really a matter of time for him.”

Kurdish and Arab security officials in northern Iraq said they also could not confirm the report.

Al Sumariya TV cited a local source in the northern province of Nineveh saying that Baghdadi and other Islamic State leaders were wounded on Thursday in a coalition air strike on one of the group’s command headquarters close to the Syrian border.

The channel has good connections with Shi’ite politicians and Iraqi forces engaged in the battle against Islamic State.

There have been several reports in the past that Baghdadi, whose real name is Ibrahim al-Samarrai, was killed or wounded after proclaiming himself caliph of all Muslims two years ago.

In the last audio message, posted at the end of December on Twitter accounts that had published Islamic State statements previously, Baghdadi said the air strikes carried out by Russia and the U.S.-led coalition had failed to weaken the group.

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The ultra-hardline Sunni group is under increased pressure in both Iraq and Syria, and the territory under its control has shrunk significantly since 2014, limiting the potential for its leaders to move around or seek shelter.

The U.S. earlier this year announced an intensification of the war on Islamic State with more air strikes and more American troops on the ground to advise and assist allied forces.

The U.S.-led coalition has regularly flown raids out of Erbil, the capital of Iraq’s Kurdistan region, in operations aimed at killing and capturing Islamic State leaders.

A Kurdish intelligence official and an Arab from the Baaj area west of Mosul said the U.S.-led coalition had conducted such a raid there earlier this week. The coalition did not confirm this raid.

Kurdish Peshmerga forces are positioned in an arc around the north and east of Mosul while the Iraqi army is trying to capture Falluja, 50 km (30 miles) west of Baghdad.

The army’s elite Counter Terrorism Service was battling on Friday in al-Shuhada, a southern district of Falluja, a Reuters photographer reported from the scene.

Loud explosions and bursts of gunfire were heard from the district, while aircraft believed to belong to the U.S.-led coalition flew overhead.

Al-Shuhada marks the first advance of the army inside the built-up area of Falluja, after two weeks of fighting on the outskirts to complete the encirclement of the city.

The encirclement was completed with help from Iran-backed Shi’ite militias. They deployed behind the army’s lines and did not take part directly in the assault on the city to avoid inflaming sectarian feelings.

A government official said Islamic State militants are putting up a tough fight defending the city that stands as a symbol of the Sunni insurgency that followed the U.S. occupation of Iraq, in 2003.

Prime Minister Haider al-Abadi said the troops are progressing cautiously in order to protect tens of thousands of civilians trapped in Falluja.

The United Nations says 90,000 civilians may have remained in Falluja, under “harrowing” conditions with little access to food, water and healthcare, and no safe exit routes.

The insurgents have dug a network of tunnels to move around without being detected and planted thousands of mines and explosive devices to delay the army’s advance.

Finance Minister Hoshiyar Zebari said a week ago that the battle of Falluja “will take time”.

The Iraqi army is also massing tanks and troops south of Mosul, in preparation for an offensive planned later this year to retake the largest city under the control of the militants.

In Syria, Russian- and Iranian-backed Syrian government forces and U.S.-backed Syrian opposition and Kurds are separately trying to advance on Raqqa, the group’s capital in Syria.