AFP correspondent at the scene said.
A Kenyan security source said an assault against Al Qaeda-linked Somali gunmen inside the complex was underway.
The AFP correspondent said he heard about 15 minutes of fierce gunfire which then subsided. An AFP photographer at the scene said troops posted around the mall ducked for cover.
The photographer said it was "sounded as if the shots were coming from somewhere around the mall, or were being fired from a vantage point in the mall."
The Kenyan army had earlier said it had managed to isolate the Islamist attackers, who stormed the complex at midday on Saturday, killing at least 68 people and taking hostages. Around 200 people were also wounded.
The army had described the operation as "delicate" because the gunmen were holding a number of hostages.
Shebab rebels said its fighters had carried out the attack in retaliation for Kenya's military intervention in Somalia, where African Union troops are battling the Islamists.