The Shabab has said it was responsible for the assault on Westgate, which saw a group of gunmen walk into the part Israeli-owned mall at midday Saturday and gun down shoppers and staff.
Another Shabab message said it had been "a great pleasure to have had you completely enthralled for more than 100 hours. What a wonderful audience you've been!".
It also boasted that the "Kenyan government is still in disarray", saying it "won't be until several months when it fully comprehends exactly what took place at Westgate".
Shabab chief Ahmed Abdi Godane said the Nairobi mall carnage was retaliation for Kenya's military intervention in Somalia.
Kenya invaded southern Somalia to attack Shabab bases two years ago, and later joined the 17,700-strong African Union force deployed there.