It said it was seeking to bring a "speedy conclusion" to the siege.
"Our concern is to rescue all hostages ALIVE and that is why the operation is delicate," the Kenya Defence Forces said in a situation update on Twitter.
The assault by Kenyan forces, which began shortly before sundown, came as two helicopters circled the mall, with one skimming very close to the roof.
A loud explosion rang out, far larger than any previous grenade blast or gunfire volley.
Kenyan police said on Twitter that a "major" assault had started to end the bloody siege.
"This will end tonight. Our forces will prevail. Kenyans are standing firm against aggression, and we will win," Kenya's National Disaster Operation Centre said on Twitter.
AUSSIE AMONG VICTIMS
A dual Australian-UK national is among the victims of the unfolding Nairobi shopping mall siege, the Department of Foreign Affairs and Trade says.
"Advice received from the Australian High Commission in Nairobi confirms that an Australian-UK dual national was among those killed in the terrorist attack on the Westgate shopping mall in Nairobi," a DFAT spokeswoman told AAP late on Sunday.
"The Australian government deeply regrets this senseless loss of life and extends deepest sympathies to the family of the victim.
"It is not appropriate to name the individual."
Consular assistance will be extended to the family of the person killed, but no identifying details have been released.
At least 68 people were killed and 175 wounded when al-Qaeda-linked Somali militants stormed an upmarket shopping centre in the Kenyan capital, according to local officials.
Between 10 and 15 gunmen are believed to be holed up in the building with an unknown number of hostages, a full day after the carnage began.
DFAT says it's received confirmation that two Canadian nationals have been killed, including a diplomat, and the French government has advised that two of its nationals are among the victims.
One New Zealand national has been confirmed as injured.
"The situation on the ground remains fluid," DFAT's spokeswoman said.
"DFAT has received advice from several Australians who were caught up in the attack and managed to escape to safety."
Among them is Melbourne woman Sarah Williamson, who reportedly survived by huddling in a phone store.
The 23-year-old was in the mall with her father, who works for the UN, when she heard the first explosions.
"She heard the first grenade go off and said, `What was that, dad?'," her mother Linda has told Fairfax Radio Network.
"Then he heard the guns firing and he knew exactly what it was and he said, `We're under attack, everybody to the back of the room.'"
The Eltham woman spent six hours trapped in the store before she could run to safety.
Foreign Minister Julie Bishop has condemned the terrorist attack and expressed her sympathy to Kenyans and President Uhuru Kenyatta, who has lost family members in the incident.
"The thoughts of all Australians are with the victims and their families," she said in a statement.
Prime Minister Tony Abbott was briefed on the unfolding crisis earlier on Sunday.
Australians still in Kenya have been urged to avoid all public places in Nairobi for the next 24-48 hours and closely monitor local media.
People with concerns about family or friends in Kenya should try to contact them directly or if unsuccessful phone the DFAT consular emergency centre on (02) 6261 3305.
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