"We will... stop at nothing to avenge the deaths of our Muslim brothers until your government ceases its oppression and until all Muslim lands are liberated from Kenyan occupation," the Shebab said in a statement.
"And until then, Kenyan cities will run red with blood... this will be a long, gruesome war of which you, the Kenyan public, are its first casualties."
The day-long siege on Thursday of the university in the northeastern town of Garissa was Kenya's deadliest attack since the 1998 bombing of the US embassy in Nairobi, and the bloodiest ever by the Shebab militants.
Survivors who hid from the attack have recounted how the gunmen called on people to come out of their dormitory bedrooms and lie on the ground face down, but then killed them.
A photograph seen by AFP from inside the building showed over 50 students killed lying down on the ground.
"The mujahedeen stormed the university compound and swiftly proceeded to the halls of residence where they had gathered all the occupants," the statement added.
The statement also 0described what it called "unspeakable atrocities against the Muslims of East Africa" by Kenyan security forces, both in Kenya's northeastern ethnic Somali region and in southern Somalia, when Nairobi sent troops in 2011 to battle the Islamists.
The Kenyan government has vowed that it would not be "intimidated".
But the Shebab also warned the public they would be targeted in "schools, universities, workplaces and even in your homes" as they had elected the government.

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