Rhinos are often moved when their populations outgrow their surroundings.
A Kenya Wildlife Service (KWS) official who did not want to be named said the seven rhinos which were being moved from Nairobi National Park to Tsavo East National Park died in unclear circumstances but noted that efforts are underway to establish the cause.
The relocation of endangered animals - known as translocation - involves putting them to sleep for the journey and then reviving them in a process that carries risks.
The tourism ministry said "preliminary investigations" suggested the rhinos could have died of "salt poisoning" after drinking different water in their new environment.
Officials must take responsibility for the deaths and explain what went wrong during the relocation, conservationist Paula Kahumbu said, according to The Guardian.
"Rhinos have died, we have to say it openly when it happens, not a week later or a month later. We have to find out what's gone wrong, so that these mistakes are never repeated".
The wildlife ministry said "disciplinary action will definitely be taken" if an investigation into the deaths indicates negligence by agency staff.
Poachers hunt black rhinos for their horns, which are coveted for traditional Chinese medicinal practices and are displayed as status symbols. "Rhino translocations also have major welfare considerations and I dread to think of the suffering that these poor animals endured before they died".
In May, six black rhinos were moved from South Africa to Chad, restoring the species to the country in north-central Africa almost half a century after it was wiped out there.
"At a time when three rhinos are poached on average a day for their horns, any losses are particularly painful", WWF Kenya CEO Mohamed Awer said in a statement to CNN.
With a goal of bringing them back, Dean said Kenya aims to increase the number of black rhinos by 2,000.
In the national Park of Kenya has claimed the lives of eight black rhinos that are under threat of extinction, according to the government of the country. Three were shot dead inside a protected sanctuary in northern Kenya in May.
Dean said there were once thousands of black rhinos in Kenya but now their population is in the hundreds.