The two countries also offered assistance in the investigation.
Mr Msando’s family have urged the Kenyan government to accept the offer in order to conclude the matter with urgency.
“We are deeply devastated at the tragic loss,” the family said in a statement.
“Chris Msando was a loving family man, who cherished and adored his wife and children.”
The family also asked social media users to be mindful of what they post, saying: “A lot of the information out there is false and meant to injure and paint the family in a bad light.”
An autopsy on the body of the woman found alongside Mr Msando, thought to be that of his companion Carol Ngumbu, will take place on today.