The rebels said the carnage was in direct retaliation for Kenya's military intervention in Somalia, where African Union troops are battling the Islamists.
"The Mujahideen entered #Westgate Mall today at around noon and are still inside the mall, fighting the #Kenyan Kuffar (infidels) inside their own turf," the group said on Twitter.
A security source said police and soldiers had finally "pinned down" the gunmen after hours of fierce gunbattles and painstaking evacuations, with police going shop to shop to secure the Westgate shopping mall.
Senior police sources described the attackers as a well-organised "terror gang" numbering around 10. The mall, popular with wealthy Kenyans and expatriates and part Israeli-owned, was packed with around 1,000 shoppers when it was besieged at midday.
The Shebab tweet said the group's warnings over Kenya's military presence in Somalia had been ignored.
Shebab "on numerous occasions warned the Kenyan government that failure to remove its forces from Somalia would have severe consequences," it said.
"The attack at #WestgateMall is just a very tiny fraction of what Muslims in Somalia experience at the hands of Kenyan invaders," it said.
Kenyan forces entered Somalia two years ago to fight the Shebab, and remain in the country as part of an African Union force that is supporting Somalia's internationally backed government.
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