Volgograd is still in mourning until Friday after two bombings which killed 34 people. Five of the 62 wounded are critically ill in hospital.
Russian security forces have detained more than 700 people.
The BBC reports thousands of police officers are checking people on public transport, stopping cars and questioning drivers as well as individuals at markets and shops.
Cossacks and volunteers known as druzhinniki are patrolling the streets and checking buses.
Interfax news agency reported that investigators believe that both suicide bombers were men who came from the North Caucasus.
The first bombing took place at the main railway station on 29 December and the second the following morning was on a trolleybus during rush hour.
The city was called Stalingrad in Soviet times.