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Kenyan authorities have detained a foreigner over the murder of a 20-year-old Kenyan student.

He was arrested on Tuesday as he attempted to leave Kenya on a Mozambican passport, authorities say.

Rita Waeni's dismembered body was found last Sunday at a short-term rental apartment in the capital Nairobi.

Her family now says they believe that "she was lured by her killer, who also tried to extort money from her family, even after killing her".

The killer sent three messages from Ms Waeni's phone on Sunday morning, demanding that her family pay a ransom of 500,000 Kenyan shillings ($3,100; £2,400) within 24 hours to secure her release, her family revealed on Wednesday.

Her decapitated body was found shortly afterwards.

"Unfortunately, the family did not get further details about the ransom or an opportunity to explore this route. Additionally, some demands were made when she had already been murdered," a family representative said in a statement on Wednesday.

Police are looking for Ms Waeni's head, which was taken by her killer, along with her phone and other personal items.

In the statement, the family said their lives have been shattered by the killing, "and especially by how she was killed".

Police are also trying to match the suspect to a man captured by security cameras picking up the keys to the rental apartment.

Two other persons of interest have been arrested in connection with the killing.

Investigators - who have gained access to Ms Waeni's Instagram account - say that the killer lured her through the social media app.

She was entering her final year of studies at the Jomo Kenyatta University of Agriculture and Technology.

Ms Waeni's brutal murder, the latest in a spate of killings of women, has shocked and angered many Kenyans, igniting an online campaign calling for the protection of girls and women.

Less than two weeks ago, a Kenyan socialite was also murdered in a similar setting.