In a taped statement on al-Iraqiya TV, Rasool said the Iraqi Army's 9th Armored Division had reached the banks of the Tigris River in the city, with the 16th Infantry Division fast approaching.
The remnants of ISIS' army were under siege, and more than 35 fighters and commanders were killed during fighting on the riverbanks, Rasool said. The river marks the final few blocks of western Mosul still under ISIS control.
"Victory is very near," Rasool declared.
The capture of 35 ISIS fighters trying to flee along the riverbanks signaled the collapse of the terrorist group's destructive hold on Mosul, Rasool said. Troops were just meters (yards) from spots where the last fighters were holed up.
"We are achieving huge victories," Rasool said.
A declaration of victory was expected soon from Iraqi commanders and Prime Minister Haider al-Abadi, whose government in Baghdad had come under increasing political pressure to announce the end the operation, according to al-Iraqiya TV.
Brigadier General Walid Khalifah, deputy commander of the 9th Armored Division, told al-Iraqiya TV that his troops were hours away from taking "complete control" of the Shahwani area.
The 16th Infantry Division and anti-terrorism forces had come together after successfully completing their missions, the general said.
"We have drones over the area and we watch (ISIS) fighters running away," Khalifah told the station.
Commanders have warned it will take time to clear the regained areas of booby traps and explosives left by militants.
In anticipation of the victory, Iraqi soldiers and federal police -- waving weapons and carrying flags -- danced on he rubble-strewn streets of Mosul's Old City, according to video footage from the scene.
The long-awaited celebration comes three years after the terrorist group swiftly overran the city
as security forces dropped their weapons and fled with civilian masses.
And the triumph comes at a steep price. Saturday, a number of civilians were killed when ISIS fighters blew up three houses where they were holed up with families used as human shields in the Old City's al-Nujaifi area, Col. Abdulrahman al-Khazaali, a federal police spokesman, told CNN.
At least 30 civilians, including women and children, were rescued from the houses, with some pulled from the rubble, he said.
Soldiers rescued crying babies and children from damaged homes, cradling them and giving them water as bursts of gunfire erupted in the background, according to video released by the federal police.
The ISIS-affiliated Amaq news agency said remnant fighters in the Old City have pledged to fight to the death.
The road ahead
The retaking of Mosul will leave the Iraqi military to confront ISIS elsewhere in Iraq. The group still controls cities in Kirkuk, Nineveh and Anbar provinces, including Hawija, Tal Afar, Qaim, Ana and Rawa.
And Baghdad will have to hold onto Mosul, rebuild its infrastructure and prove it can effectively govern it.
When the ISIS militants raided
Iraq's second-largest city three years ago, a stunned world watched as the terrorist group freed hundreds of prisoners and took over military bases, police stations and banks.
Mutilated bodies of soldiers, police officers and residents lay scattered in the streets as the militants raised the ISIS flag on public buildings
At the time, witnesses described scenes of buildings and boulevards manned by the terrorist group instead of the usual Iraqi forces.
Al-Abadi, in October last year, announced the start of the mission to retake Mosul using a diverse coalition of about 100,000 troops.
The city is 560 kilometers (350 miles) northwest of Baghdad. It was considered one of the main entry points for foreign fighters coming into the country.
For three years, as foreign fighters poured into Mosul, hundreds of thousands of residents fled -- prompting a refugee crisis because they were either internally displaced or living in foreign lands.
Iraq is now left to address the humanitarian crisis and ease the flow of refugees into neighboring countries
ISIS took control of more than 2.5 million people and unleashed a reign of terror.
It beheaded people in public, threw gay men to their deaths from the top of buildings and made prisoners out of men who did not grow beards and women who did not wear Islamic clothing such as burqas.
Mosul's location is incredibly important. It's a key trading city not far from the borders of Syria and Turkey. Wresting Mosul away from ISIS significantly limits the movement of fighters, weapons and supplies.
The city is also near some of Iraq's most vital oil fields, as well an oil pipeline that services Turkey. Securing these fields could bolster Iraq's economy and also hit ISIS' finances hard as the militant group sells oil illegally to fund its operations.