Iraqi forces hit further pockets of resistance from Islamic State militants in Mosul's Old City on Friday, four days after the prime minister declared victory.
Army helicopters flew overhead and explosions could be heard, residents said.
"Three mortars landed on our district," a resident of Faysaliya, just across the Tigris river in east Mosul, said by telephone.
The U.S.-led coalition backing the Iraqi military campaign said it had conducted two air strikes in the Mosul area a day earlier, destroying 22 fighting positions and a tunnel.
The victory of U.S.-backed Iraqi forces in Mosul marked the biggest defeat for Islamic State, which is also under siege in the eastern Syrian city of Raqqa, its operational base.
A few hundred Islamic State insurgents swept into Mosul three years ago as the Iraqi army collapsed, imposing a reign of terror and declaring a caliphate in territory it had seized spanning swathes of Iraq and Syria.
The group still controls areas south and west of Mosul inhabited by tens of thousands of people. The top U.S. general in Iraq said this week that security forces would rest and re-equip before moving on to Tal Afar, 65 km (40 miles) west of Mosul.
The United Nations on Friday estimated that than 20,000 people remained in the city, whose pre-war population were mostly Shi'ite and Sunni Turkmen.
Iraqi forces have regained control of more than half of Imam Gharbi, a village south of Mosul that Islamic State militants armed with machine guns and mortars stormed last week, a security source said. A few dozen insurgents are estimated to remain in the area.
Securing long-term peace in Iraq will not be easy.
Prime Minister Haider al-Abadi faces the challenge of preventing revenge killings that could create more instability, as well as stemming the sectarian tensions and ethnic strife that have dogged Iraq since a U.S.-led invasion toppled Saddam Hussein in 2003.
On Thursday, Human Rights Watch said it had used satellite imagery to verify that a video published on Facebook on Tuesday, showing armed men in military uniforms beating a detainee before throwing him from a precipice and then shooting at him, had been filmed in west Mosul.
The footage also shows the men shooting at the body of another man already lying at the bottom of the precipice.
Reuters could not independently verify the footage. Since the victory announcement, security forces have severely restricted media access to west Mosul, saying they need to remove or defuse explosive devices.
In his first Friday sermon since the proclamation of victory in Mosul, Grand Ayatollah Ali al-Sistani, Iraq's top Shi'ite cleric, urged his compatriots to avoid violence and sectarianism.
Iraq's joint operations command said the allegations were being looked at closely and if any violations were found, those responsible would be held accountable. It also said that the videos could have been fabricated.
Three other videos posted this week by the same account appear to show members of various Iraqi security forces beating men wearing ordinary clothes. Reuters could not independently verify the footage.
Human Rights Watch also accused the security forces of forcibly relocating at least 170 families of alleged Islamic State members to a closed "rehabilitation camp" as a form of collective punishment.