Businessmen angrily criticised the government for failing to stamp out gangland murders, a failure Mr Chernomyrdin himself acknowledged in calling on Monday for a crackdown on organised crime.
The Prime Minister was among several hundred mourners at the mayor's office in Moscow, where Kivelidi's body lay in state. The mayor, Yuri Luzhkov, and two senior aides to President Boris Yeltsin, Georgy Satarov and Alexander Livshits, also attended. Mr Yeltsin sent a message of condolence.
Dozens of bodyguards and policemen stood by to protect the politicians and businessmen, who arrived in shiny Volvo and Mercedes cars. The crackle of radios and the beep of cellular phones broke into the solemn music played over loudspeakers.
Wearing a black armband on his navy suit, Mr Chernomyrdin added a bunch of red roses to the sea of wreaths and flowers around the coffin and stood for a few moments in silence near Kivelidi's family. Several hundred mourners, some clutching icons, attended the burial later at the Vagankovskoye cemetery.
Sergei Yushenkov, a liberal MP, said Kivelidi's killing did not appear to be politically motivated. But the presence of Mr Chernomyrdin and other senior politicians at the service indicated government recognition that Russia's spiralling murder rate must be stopped. Most of the 500 recorded contract killings in Russia last year remain unsolved.
Kivelidi, 46, the most prominent businessman to be killed in Russia this year, died on Friday in a poisoning that also killed his secretary. Newspapers reported that the poison, believed to be the salts of a heavy metal such as cadmium, was slipped into their tea and smeared on a telephone. Kivelidi headed both Rosbiznesbank, a leading bank, and the Russian Business Round Table, the country's most influential business organisation, with close ties to Mr Chernomyrdin.
Vladimir Shcherbakov, the deputy head of the Round Table, dismissed the latest government promises to take on criminal gangs. "It's worse than Chicago [in the 1920s]," he said. "There, gangs just shot at each other - here, a black, corrupt type of business is destroying civilised life."
According to Mr Shcherbakov, whose organisation represents the 200 largest businesses in Russia, there were 90 attacks on businessmen in the past year, in which 46 were killed. Nine of the Round Table's own senior members were among the murder victims. "Not one conviction has been made," he said. "No one has enough security to protect themselves against snipers or poison."
Kivelidi frequently criticised the Interior Ministry for its failure to protect businessmen and investigate their murders. He condemned the killing of Oleg Kantor, head of the Yugorsky Bank, who was stabbed to death last month.
On Monday a restaurant manager and his seven-year-old daughter died when the businessman's car was blown apart by a powerful bomb in the Far Eastern port of Vladivostok.