New CCTV footage shows armed men carrying weapons and searching areas leading off a storeroom
'I played dead'
Somalia and Kenya: Blood brothers
Four men believed to have been involved in the deadly shopping centre attack in Nairobi last month have been named.
The Kenyan military said Abu Baara al-Sudani, Omar Nabhan, Khattab al-Kene and Umayr - shown in new CCTV footage - were killed during the standoff.
Kenya said previously 10-15 militants had been involved, but the police chief says the figure may now be four to six.
The al-Shabab group said it carried out the attack on the Westgate mall on 21 September, leaving at least 67 dead.
The al-Qaeda-linked group said the attack was in retaliation for Kenya's military involvement in Somalia.Too early?
The naming of the men came as CCTV footage was aired showing four attackers calmly walking through a room in the mall holding machine guns.
Kenya Defence Forces spokesman Maj Emmanuel Chirchir told Reuters news agency: "I confirm these were the terrorists; they all died in the raid."
Kenya: Major attacks
1998: US embassy in Nairobi bombed, killing 224 people - one of al-Qaeda's first international attacks
2002: Attack on Israeli-owned hotel near Mombasa kills 10 Kenyans; simultaneous rocket attack on an Israeli airliner fails
2011: Suspected al-Shabab militants raid Kenyan coastal resorts and a refugee camp, targeting and kidnapping foreigners
2011: Kenya sends troops into Somalia to tackle al-Shabab
2011-13: Numerous grenade attacks near Somali border and in Nairobi
How the attack happened
Horror and heroism
Reuters quoted Maj Chirchir as saying that al-Sudani was an "experienced fighter" from Sudan and was believed to be the leader of the group.
Maj Chirchir said Nabhan was a Kenyan of Arab origin and al-Kene a Somali linked to al-Shabab. Further details about Umayr had not yet been verified, he said.
Kenyan police chief David Kimaiyo told Kenya's KTN television station it was now believed that four to six gunmen had carried out the attack, not 10-15.
"None of them managed to escape from the building after the attack," he said.
Kenya had earlier said five attackers were killed in the security operation and that nine people were in custody.
The BBC's Gabriel Gatehouse in Nairobi says the latest CCTV footage is from a limited part of the complex and, with some eyewitnesses reporting a two-pronged attack, it is too early to say definitively how many gunmen were in the building.
In addition to the 67 people killed in the attack, a further 39 are still missing, according to the Kenyan Red Cross.
Al-Shabab is banned as a terrorist group by both the US and the UK and is believed to have between 7,000 and 9,000 fighters.
Its members are fighting to create an Islamic state in Somalia.
About 4,000 Kenyan troops were sent to Somalia in October 2011 to help pro-government forces end two decades of violence, with clan-based warlords and Islamist militants all battling for control of the country.
On Saturday, Islamist fighters in southern Somalia said Western forces had launched a night-time raid on one of their bases.
No-one has admitted the attack. US and French special forces have carried out raids in Somalia in recent years.
It is not clear whether the raid was linked to Westgate.