Iraq state TV aired live footage showing thick black smoke rising from the Old City, with the sound of gunfire rattling inside. It said leaflets were distributed urging civilians to leave through five "safe corridors."
The International Rescue Committee called on Iraqi forces and the U.S.-led coalition to "do everything in their power to keep civilians safe during these final stages of the battle for Mosul."
"With its narrow and winding streets, Iraqi forces will be even more reliant on airstrikes despite the difficulty in identifying civilians sheltering in buildings and the increased risk of civilians being used as human shields by ISIS fighters," said Nora Love, the aid group's acting country director, using another acronym for IS.
The Islamic State group captured Mosul when it swept across northern and central Iraq in the summer of 2014. Iraq launched a massive operation to retake the city last October, and has driven the militants from all but a handful of neighborhoods.
Love warned that the assault on the Old City could lead to even more civilian deaths than the hundreds killed so far in airstrikes across the rest of the city, as "the buildings of the old town are particularly vulnerable to collapse even if they aren't directly targeted."
Those who try fleeing to government-controlled areas risk being caught in the crossfire or targeted by IS snipers, Love added.
Gen. Abdel Ghani al-Asadi, the head of Iraq's special forces, told state TV he expects the extremists to put up a "vicious and tough fight." Al-Asadi said the troops "will be very careful" to protect the civilians.
The Old City is home to the centuries-old al-Nuri mosque, where IS leader Abu Bakr al-Baghdadi delivered a Friday sermon in 2014 as his group declared an Islamic caliphate in the areas it controlled in Syria and Iraq. The militants have lost much of that territory over the last three years, and Mosul is their last urban bastion in Iraq.
Up to 150,000 civilians are believed to be trapped in the Old City, where the militants are using them as human shields, U.N. humanitarian coordinator Lise Grande told The Associated Press on Friday. She said conditions are "desperate," with little food and no clean water.