Counter-terrorism service (CTS) forces pushed across a tributary of the Tigris river shortly after midnight and drove back Daesh militants in the Muthanna district, CTS spokesman Sabah al-Numan said.
"We used special equipment and had the element of surprise; the enemy did not expect us to mount a night offensive because all previous offensives were during the day," Reuters quoted him as saying.
A second phase of the nearly 12-week campaign to drive Daesh out of its last major city stronghold in Iraq began last Thursday.
The large-scale military operation to retake Mosul, which began on October 17, 2016, included 30,000 Iraqi soldiers backed by Hashid al-Shaabi (voluntary) and Kurdish fighters. Mosul has been occupied by Daesh since 2014.