The so-called Islamic State group has released an audiotape which it says is from its leader, Abu Bakr al-Baghdadi.
If true, it would be the first public message from him in about a year and would dispel rumours that he is dead.
The voice on the audio calls on Iraqis to defend the city of Mosul against the Iraqi army, which is attempting to re-take it from the militants.
Baghdadi’s whereabouts remain unknown. Some officials have said he may be inside Mosul alongside IS fighters.
It has not been independently verified that the voice in the audio belongs to Baghdadi. There have been repeated rumours of his death through the years, including last year when the Iraqi military said it had hit his convoy.
Mosul, the last IS urban stronghold in Iraq, is where Baghdadi declared a caliphate two years ago.
Iraqi special forces are consolidating their most recent gains in the offensive, with the help of Kurdish Peshmerga forces, Shia militias and Sunni Arab tribesmen.
On Wednesday they were combing the streets for any remaining IS fighters in the recently recaptured Kukjali district, in the east, before they press on into the heart of the city.
Earlier, Amnesty International said there was increasing evidence that some of the Sunni militia groups were carrying out reprisal attacks on local men and boys suspected of links to the IS jihadists.
In the message released early on Thursday, a voice says: “Holding your ground with honour is a thousand times easier than retreating in shame.”
“Do not retreat,” it says. “this total war and the great jihad only increased our firm belief, God willing, and our conviction that this is all a prelude to victory.”
The voice calls on people in Nineveh, the Iraqi province where Mosul is located, to fight the “enemies of God”.
It also calls for more IS sympathisers to attack other countries, saying suicide fighters should “turn the nights of the unbelievers into days, to wreak havoc in their land and make their blood flow as rivers”.
A collection of Iraqi forces backed by an international coalition launched an offensive on Mosul on 17 October, the latest attempt to wrest land back from IS.
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In addition to Kukjali, Iraqi counter terrorism forces retook the more built-up Karama district on Tuesday.
The BBC’s Ian Pannell, who was travelling with them, says those militants who chose to stand and fight were killed while others fled deeper into the city.
Amnesty International says people suspected of having ties to IS have been beaten, given electric shocks or dragged through the streets by cars, according to eyewitnesses on the ground.
The human rights group said it was the Sunni tribesmen – specifically the Sabawi Tribal Mobilisation – who are alleged to have been involved in revenge attacks in the south-east of Mosul in recent weeks.
Lynn Maalouf from Amnesty said there was a “dangerous culture of impunity in which perpetrators of such attacks feel they have free rein to commit crimes and go unpunished”.
She urged the Iraqi authorities to control the tribal militia fighters responsible for the attacks and “bring them to justice”.
There are concerns for the estimated 1.2 million civilians who remain inside the city, with the Norwegian Refugee Council warning that there lives are in “grave danger” due to the fighting.
Some have fled to a camp for internally displaced people, east of Mosul.
Mosul battle: ‘IS leader Baghdadi’ urges no retreat