Others said they wanted to know if their relatives had died, but feared they were not being told.
The power plant, one of the world's biggest, lies some 3,000 km (1,875 miles) east of Moscow. It has now stopped working.
The dam is 245m (800ft) high and stretches 1km (0.6 miles) across the Yenisei river.
The explosion flooded a turbine hall and destroyed three generating units.
Divers are examining the debris in the hall and searching for bodies, in icy water.
Emergencies Minister Sergei Shoigu said it would take at least a week to assess damage in the flooded hall.
The blast's cause is unknown but reports said investigators believed a transformer exploded during repairs.
The plant's owner said the flooding had occurred due to a pressure surge in water pipes.
Wednesday is an official day of mourning in the remote mountain region of Khakassia where the plant is located.
RusHydro said the damage would run into "billions of roubles" and take several months to repair.
Mr Shoigu said repairing the turbine hall alone could cost 40bn roubles ($1.3bn; £762m).
But he said it would still be worth doing the repairs, because the dam - undamaged by the blast - had accounted for 80% of the construction cost.
Opened in 1978, the station provides a quarter of RusHydro output and is a major power supplier to at least two smelters owned by United Company RUSAL, the world's largest aluminium producer.
SCO supports Russia in suppression of terrorist activity in the North Caucasus
text: Kazakhstan Today
Shanghai Cooperation Organization (SCO) supports Russia in suppression of terrorist activity in the North Caucasus. SCO Secretary General, Bolat Nurgaliev, said in connection with terrorism act in Nazran, Kazakhstan Today agency reports citing SCO official site.
"SCO member states are solidary with the actions undertaken by the Russian authorities to suppress terrorist activity and safety and stability in the country," B. Nurgaliev said.
"In connection with the act of terrorism in Nazran (the Republic of Ingushetia of the Russian Federation), that have entailed numerous human victims, we condole with the victims' families."
One killed, one injured in south Russia blast
MOSCOW, August 20 (RIA Novosti) - One man was killed and another severely wounded when an explosive device went off in south Russia's Republic of Kabardino Balkaria, a local police official said on Thursday.
"A man died at the scene as a result of the explosion, and another man was taken to hospital with multiple injuries," the official said, adding that police resumed an examination of the scene this morning.
Russia's North Caucasus region has been swept by a wave of militant violence in recent months.
Ingushetia, which borders Chechnya, saw its deadliest attack in years on Monday, when a suicide bomber driving an explosives-laden minivan rammed the gate of the police headquarters in Nazran, killing 24 people and injuring 136.