This was announced by doctor Volodymyr Halyk of the 17th city hospital in Kyiv, Censor.NET reports citing Ukrainski Novyny.
He said both Osmaev and his killer are in the emergency room of the hospital.
"Their condition is stable with some positive dynamics," the doctor said.
Both wounded have signs of being conscious.
The doctor said that Okuev's gunshot wounds were penetrating, while the attacker still has one bullet remaining in his body. It will be extracted later.
"All necessary operations have been done. We are working to keep them alive and sound. They are in the emergency room, on mechanical ventilation, but both have signs of being conscious," 112 Ukraine cited Halyk as saying.
The doctor said the patients are not able to talk, so no questioning has been done so far.
In the evening of June 1, an attempt was made on the lives of Chechen volunteer fighters of Ukrainian Kyiv-2 unit, Donbas war participants Adam Osmaev and Amina Okueva in Kyiv's Podil district.
Related materials: Attempt on Osmaev