Eyewitness reported a huge blast from inside the Westgate mall where the attackers had been holed up since shooting their way into the shopping centre on Saturday.
The explosion was the loudest heard since the attack began and was followed by a long silence.
The Kenyan government's Disaster Operation Centre said late last night: "This will end tonight. Our forces will prevail."
Meanwhile, David Cameron warned the UK to brace itself for more bad news after the deaths of three British nationals in the Nairobi attack were confirmed.
The Prime Minister said the UK had offered Kenya assistance in response to the rampage by Islamic extremists in an upmarket shopping centre which left dozens dead and many more injured.
Somali-based militant group al Shabaab claimed responsibility for the attack on its Twitter feed.
Before the government attack last night it was believed up to 15 gunmen were holdingcaptives more than 24 hours after the violence began.
Mr Cameron said: "It is an absolutely sickening and despicable attack of appalling brutality.
"Because the situation is ongoing we should prepare ourselves for further bad news."
Mr Cameron offered the Kenyan authorities every assistance in a call to Pesident Uhuru Kenyatta, who lost members of his own family in the attack.
He added: "These appalling terrorist attacks that take place, where the perpetrators claim they do it in the name of a religion, they don't. They do it in the name of terror, violence and extremism and their warped view of the world. They don't represent Islam or Muslims in Britain or anywhere else in the world."
He added: "The first priority is to make sure we do everything for the British nationals caught up in this, so we're strengthening the consular services we have and the people we have to look after our people. We've also offered the Kenyans help in terms of policing and advice."
Foreign Secretary William Hague chaired a meeting of the Government's emergency committee Cobra to co-ordinate the response to the situation.
Labour leader Ed Miliband said: "The cold-blooded killing of innocent women, children and men is as despicable as it is shocking."
The Red Cross in Kenya said at least 68 people were confirmed dead and 175 others were wounded, while about 1000 were rescued from the mall.
Mr Kenyatta said his nephew and his fiancee were killed.
Promising retribution, he said: "Like the cowardly perpetrators now cornered in the building, we will punish the masterminds swiftly and indeed very painfully.
"I call on Kenyans to stand courageous and united. Let us not sacrifice our values and dignity to appease cowards. Our victory must be conclusive."
The mall was rocked by an explosion as the siege continued, with a heavy military presence including troops armed with rocket launchers at the scene.
Al Shabaab, also known as Harakat al Shabaab al Mujahideen, earlier tweeted that there will be "no negotiations".
The group csaid it warned the Kenyan government there would be severe consequences if it did not remove military forces from Somalia. It added: "For long we have waged war against the Kenyans in our land. Now it's time to shift the battleground and take the war to their land."
The organisation claimed it had killed more than 100 Kenyan "kuffar", a derogatory term used to describe non-Muslims.