The appeal was made in an audio recording released on the Internet and purported to be by the elusive leader of the Islamic State group, his first message this year.
"Do not retreat," he said. "Holding your ground with honour is a thousand times easier than retreating in shame."
"To all the people of Nineveh, especially the fighters, beware of any weakness in facing your enemy," Baghdadi said, referring to the northern Iraqi province of which Mosul is the capital.
The "caliphate" has been shrinking steadily since last year and Iraqi forces earlier this week reached Mosul, the jihadists' last major stronghold in Iraq.
Tens of thousands of Iraqi forces, backed by the US-led coalition and its warplanes, launched a massive offensive on Mosul on October 17.
It was not immediately possible for AFP to authenticate the recording, entitled "This is what God and his messenger have promised us", but leading experts of the jihadist organisation did not appear to doubt it.
IS has had a tendency to fall back when massively outnumbered lately, giving up some of its emblematic bastions - such as Fallujah in Iraq and Dabiq in Syria - without following its own apocalyptic ideology of fighting to the bitter end.
In his latest message, which is undated but makes references to events that are at most a few weeks old, Baghdadi calls for attacks against Saudi Arabia - a favourite target of his - and Turkey.
Ankara has troops stationed at a base just outside Mosul and Turkish President Recep Tayyip Erdogan's escalating rhetoric has raised fears of a unilateral Turkish intervention in Iraq.
He attempted to stir up sectarian resentment by referring to religious flags and slogans of Shiite fighters among the Iraqi forces and by accusing the country's Sunni politicians of treason.
The recapture of Mosul by Iraqi forces could spell the end of the group's days as a land-holding force in Iraq and deal a death blow to the "caliphate".
The US-led coalition estimates the number of IS fighters holed up in Mosul at 3,000 to 5,000 and has warned the battle of Mosul could be long and difficult.
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