The Kenyan government said that two of the attackers had been shot dead inside the mall Monday morning.
"We have this morning killed two of the attackers and our security forces are now in control," Joseph Ole Lenku, Kenya's cabinet secretary in charge of security, said in a media briefing Monday afternoon.
Terrorists of the Al Qaeda-allied Al Shabab, holed up in the mall and holding an unknown number of people hostage, exchanged gunfire with Kenyan security forces throughout Monday morning, confirming that the operation to end the siege was under way.
In a terror act reminiscent of the 26/11 Mumbai attacks in which scores of people were held by gunmen, the attackers continued the siege on the upmarket Westgate shopping mall showing no sign of surrendering even as Israeli, British and American security agents joined local security officers in trying to break the stalemate.
President Uhuru Kenyatta had pledged Sunday evening that the Islamists would not go unpunished and Kenya would not succumb to threats or intimidation from the Somalia-based militia.
"Our country is not going to give in to intimidation by terrorists (and) neither will we withdraw our security officers from our neighbour Somalia where we have helped establish some form of stability and liberated sections of the country from the militia", said Kenyatta in reference to the thousands of troops Kenya has deployed to the war-ravaged country.
A Twitter account allegedly operated by Al Shabab claimed that 10-15 men were behind the attack.
Several survivors of the terrror act described the perpatrators as ethnic Somalis and Arabs.
The gunmen had stormed the mall in the capital of the east African country Saturday morning armed with grenades and assault rifles and faces covered with the kaffiya or Arabic scarf.
The incident has had the effect of seemingly uniting the country's sharply divided political class, with opposition leader Raila Odinga standing side by side with Kenyatta at a press conference Sunday afternoon called to state the country's position on the shocking act of terror.
"I have personally lost a close relative in the heinous attack on innocent people," said Kenyatta.
"My nephew and his fiancee have lost their lives during this criminal attack on civilians," he added.
Reports indicated that among the dead are diplomatic staff from Western countries and two Indian nationals, shot by the gang that includes two women.
The Indian high commission in Nairobi could not give the identities of the victims with an employee indicating that top officials were holed up in meetings most of the day.
In New Delhi, officials named two of the Indians killed as Sridhar Natarajan, 40, from Tamil Nadu and an employee of a local pharmaceutical firm Harley's Limited; and Paramshu Jain, eight, the son of Manoj Jain, the branch manager of Industrial Area Branch, Bank of Baroda (Kenya Limited).
With some 179 people injured and being treated in hospitals in the city, Kenyans generously donated blood at appointed donation centres in a show of solidarity with the victims.
Some 1,000 people have been rescued from the mall since Saturday but the national mood was dampened Sunday evening when rescue teams emerged from the basement of the mall with nine bodies of victims.
Earlier Monday, loud explosions accompanied by gunfire were heard at the building before black smoke started billowing from the building.
Lenku said the smoke emanated from a supermarket on one of the floors of the mall , adding that the attackers had started the fire to confuse security forces.
According to Kenya's head of armed forces Julius Karangi, the terrorists were of different nationalities.
"We have clear intelligence reports that the criminals come from different nationalities... we are fighting international terrorists here," he said at a media briefing.
The entire world has condemned the attack with the UN Security Council and the European Union expressing solidarity with the country that has now fallen victim to a third act of terrorism since 1998.
The besieged mall is owned by Israeli businessmen and the Westgate attack has led to police being deployed to other malls and public places including hotels across Kenya.
Photos: Katrina Kaif, Shamita Shetty at Mumbai airport
Photos: Varun Dhawan, Alia Bhatt promote 'Badri...' on 'Dil Hai Hindustani'
In pictures: 15 facts about kissing that will surprise you
Photos: Shahid Kapoor and Mira Rajput at cafe in Bandra
Photos: Deepika Padukone, Neha Dhupia and Soha Ali Khan at event