“Thumbs up to our multi-agency team, we have just managed to rescue some hostages,” police chief David Kimaiyo said in a message on Twitter on the third day of the standoff.
“We’re increasingly gaining advantage of the attackers.”
Thick clouds of dense black smoke billowed from the complex after a series of loud explosions and heavy gunfire, an AFP correspondent at the scene said.
The area around the mall was teeming with Kenyan soldiers and armoured personnel carriers, as emergency workers and reporters were told to take cover.
Ambulances were also seen accelerating towards the scene as aircraft flew overhead.
The mall has been under siege by Al-Qaeda-linked Somali gunmen since Saturday in an attack that has killed at least 69 people, with another 63 reported missing.
A Kenyan special forces officer told AFP troops had moved in to end the siege with force.
“I saw them only once, I could not see them much,” he said. “It was hide-and-seek, hide-and-seek, hide-and-seek. In the end we had to use full force, we had to finish with these guys.”