Rescuers and investigators rushed to the site of the blast, which ripped through one of the train's carriages a few kilometres away from the town of Essentuki, officials said on Friday.
The interior ministry in Moscow said a "suicide bomber" was behind the explosion, the ITAR-TASS news agency reported. The blast was so powerful that it tore one of the train's cars in half.
Investigators from the Federal Security Service sifting through the wreckage found body parts of the suspected bomber strewn around, with a bag nearby that had contained mainly plastic explosives equivalent to 10 kilogrammes of TNT.
Television images showed one of the carriages as a mangled wreck of metal with shreds of bloodied clothing hanging from rods poking out. The roof was collapsed and the windows blown out. The other train cars looked intact.
At least 28 people died on the spot and four died in hospital in the Stavropol district, which lies north of Chechnya, emergency ministry officials in Moscow told AFP. Officials did not specify where the other four victims had died.
"We will find those who have committed this terrorist act. The earth will burn under their feet. These animals will never feel safe anywhere"
Boris Gryzlov, Interior Minister
More than a hundred people were rushed to local hospitals, eight of them in emergency care, rescue officials told new agencies. Fifty people were treated for minor injuries and released.
"We will find those who have committed this terrorist act,"
Interior Minister Boris Gryzlov vowed. "The earth will burn under their feet. These animals will never feel safe anywhere," said Gryzlov, who heads the main pro-Kremlin party that leads opinion polls ahead of Sunday's election, the ITAR-TASS news agency reported.
"We will find them and punish them according to the law," he said.
Russian NTV channel shows two
policemen looking at the wreckage
"There was a bomb in the second car of the train that went off as it approached the Essentuki station," an unnamed police source told the Interfax news agency.
Blaming the Chechens
A top lawmaker blamed Friday's blast on Chechen separatists.
"Since practically all of our attacks are linked to Chechnya,
it is clear these Chechen rebels" are responsible for the blast,
Alexander Gurov, chief of the State Duma's defence committee, told Moscow Echo radio.
Twin blasts rocked the same commuter line two months ago, killing four and injuring 32.