"The fire has been localized by firefighting crews," Gladyshev told TASS.
"Filling of the dock with water continues to finally extinguish the fire," he said, adding that the operation will last some two hours.
Gladyshev explained that the inner hull remains hermetically closed, and water will only get into the space between the inner and external hulls, where the rubber strip is on fire. So the equipment inside the sub will not be affected by water.
Zvyozdochka chief spokeswoman Nadezhda Shcherbinina said the operation on partial flooding of the dock section at the shipyard will take a few hours.
"The dock section will be flooded partially, approximately up to the sub's waterline to terminate combustion in the submarine's hard-to-reach part," Shcherbinina told TASS.
Earlier a shipbuilding source told TASS the operation to flood the dock had started.
"The gates of the dock are open, the operation to fill it with water has started," he said.
"As a result, the Oryol submarine will be partially flooded, which will make it possible to first localize and then extinguish the fire," he said, adding that there are "no other ways to put out the fire at the sub."
The report of the fire at the Oryol was received Tuesday at about 3:00 p.m. Moscow Time (12:00 p.m. UTC). The sub has been undergoing a major overhaul at the shipyard since November 2013. According to sources, rubber between the inner and external hulls of the Oryol is on fire near the 9th turbine compartment.
The Zvyozdochka shipyard's press service said earlier that the nuclear sub lying up caught fire at about 2:00 p.m. Moscow Time during welding work. All people on board - employees of the enterprise and submarine personnel - left the submarine quickly and in an organized way, no one was injured.
"It should be specially stressed that nuclear fuel from the atom-powered vessel has been unloaded, there are no armaments on board the vessel," the press service said.
Zvyozdochka spokesman Yevgeny Gladyshev said the submarine's interhull space caught fire near the 9th compartment. Insulation rubber covering is ablaze.