Cyrus Oguna told media that most of the hostages have been rescued. This was further confirmed by a KDF post on twitter: "Security forces have taken control of most parts of the building," Xinhua reported.
The latest development came more than 30 hours after masked gunman carried out shooting spree in the mall on Saturday morning.
The attack has left at least 68 people killed and more than 175 others injured, according to the government, the bloodiest one since the bombings at the US embassy in Nairobi in 1998.
The attack has left at least 68 people killed and more than 175 others injured
"All efforts are underway to bring this matter to a speedy conclusion," KDF said, adding four KDF personnel sustained injuries and were taken to hospital for treatment.
According to the Kenyan government, there are 10-15 gunmen inside the mall, holding unknown number of hostages, which has made the operation "delicate".
Among the slain foreigners were Two Indians, two French nationals, two Canadians, three Britons, one Chinese and one Ghanaian.
The Somali militant group Al-Shabaab has claimed responsibility for the attack, saying it was in retaliation for Kenya launching a cross-border incursion in October 2011 into southern Somalia in pursuit of Al-Shabaab militants.
The gunmen did not propose any specific demand during the tense standoff, however, the Al-Shabaab said in its twitter handle "HSM_ Press" Saturday before it was suspended that the message sent to the Kenyan government and public "is and has always been just one: remove all your forces from our country".
Refuting the pressure from the militants, Kenyan President Uhuru Kenyatta Sunday ruled out withdrawing soldiers from Somalia, saying Kenya will not relent in its resolve to fight global terrorism.
"We went as nation to Somalia to fight the war against terror unleashed on Kenyan people, Somali people and people around the world. This is not a Kenyan war, this is an international war," Kenyatta told reporters. He was flanked by former prime minister Raila Odinga and former deputy premier Musalia Mudavadi.
"They shall not get away with their despicable, beastly acts. Like the cowardly perpetrators now cornered in the building, we will punish the masterminds swiftly and painfully," the president said.
In response to the attack, Kenyan authorities have intensified security across the country, especially along its borders with Somalia, as the security operation is still underway.
Police commanders in the country's major cities and towns confirmed Sunday that security agencies have sealed off border points and all entry points amid the hostage standoff.
Since Kenya's military intervention in Somalia, Kenya has experienced repeated terror attacks which pose a great threat to Kenya's pillar industry of tourism.
Kenya's tourism has suffered a decline in tourist arrivals since September 2011, when the Somali militant group Al-Shabaab carried out the kidnappings of tourists in the Lamu archipelago and the kidnapping of the Spanish volunteers.
The terror attack at the mall which is frequented by wealthy Kenyans and foreigners would be likely to deal a blow to the sector.
Kenyatta urged Western governments not to issue warning to their citizens against visiting Kenya as it would damage the country's tourism and economy.