According to RIA Novosti, earlier Budanov said that he would like to visit Sevastopol. In his opinion, Crimeans are people "with a modified psyche" who are subject to "fair responsibility".
The head of Ukrainian intelligence also threatened some Crimeans with physical destruction.
Sheremet, in response, said that Budanov "looks like a real zombie from American horror films" who "hates humanity and all living things."
"It is useless to treat such people for dementia, only an aspen stake or its modern analogue - the Dagger rocket - will help," the deputy told the agency.
He also called the behavior of officials in Kiev "the agony of temporary workers."
The governor of Sevastopol, Mikhail Razvozhaev, said earlier that Kirill Budanov would be able to come to Sevastopol only if a tribunal over Ukrainian criminals was held in the city.
In April, Moscow's Lefortovo Court arrested Kirill Budanov in absentia on charges of organizing terrorist attacks in Russia. He is on the international wanted list.
In an interview with Yahoo! News, the Ukrainian military noted that Kiev "has killed and will kill Russians anywhere in the world."