Obama said it would be a "difficult fight," with both advances and setbacks.
The United States will be involved in ensuring humanitarian aid for up to a million civilians who may flee the city, he said at a press conference.
The Iraqi army launched on Monday what is expected to be a lengthy offensive to dislodge the terrorist organization from the city.
Iraqi officials and local media on Tuesday reported continued advances against Islamic State on front lines around Mosul.
Military officials said troops had recaptured the town of Qaraqoush, some 15 kilometers south-east of Mosul on the east bank of the Tigris.
Islamic State militants had withdrawn from the town before the military entered it, they said, speaking on condition of anonymity.
Qaraqoush was the largest Christian settlement in Iraq before it fell to Islamic State in August 2014.
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