A man wounded when a bomber set off a blast in the city’s railway station on Sunday died overnight, bringing the toll in that attack to 18. Regional governor Sergei Bazhenov said 16 died in a trolley bus bombing on Monday.
There was no indication that any of those held was connected to the attacks.
Nobody has claimed responsibility for the blasts, but they underscored vulnerability to bombings and raised fears of attacks by Islamist insurgents whose leader has called on militants to prevent Russia hosting the Olympics in February.
Mourners laid flowers at the site of the suicide bombing that tore the bus apart.
The attacks posed a challenge to president Vladimir Putin, who oversaw a war that drove rebels from power in Chechnya over a decade ago but has been unable to quell the Islamist insurgency that erupted in its wake.
Volgograd — formerly Stalingrad — is a city of about 1 million and a transport hub for an area of southern Russia that includes Chechnya and the other mostly Muslim provinces of the North Caucasus, where the insurgency generates deadly violence almost every day.
A car bomb killed a prosecutor’s assistant in Dagestan, a hub of Islamist militancy in the Caucasus, on Tuesday, and two people were killed in a bomb blast there late on Monday, authorities said.
Putin has staked his prestige on the Games in Sochi, which lies at the Western edge of the Caucasus Mountains and within the strip of land the insurgents want to carve out of Russia and turn into an Islamic State.
He ordered increased security nationwide after the attacks, the deadliest outside the North Caucasus since a suicide bomber from a province next to Chechnya killed 37 people in a Moscow airport in January 2011.
In Volgograd, about 5,200 police and interior troops were mobilised in Operation Anti-terror Whirlwind, Interior Ministry spokesman Andrei Pilipchuk, said on state TV. He said 87 people had been detained.