Kenyan army spokesman Col Cyrus Oguna said a joint operation of Kenyan and Somali government troops was launched overnight and was "basically amphibious".
"We cannot give casualty figures at the moment, the damage has not been assessed, but I can tell you our forces are already in Kismayo."
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Temperatures will reach around 28 Celsius (82F) at their highest.
A minute's silence will be observed at 11am on Thursday in remembrance of those who lost their lives in the Manchester Arena attack.
New research has found those who consumed two cups had a 35% reduced risk, and for those who drank five cups, the risk halved.