Yesterday, Mr Konev gave an emotional press conference, describing the moment he came face to face with the intruder who is believed to have killed his "angel" Katerina.
Mr Konev, a 41-year-old English student, told how he put his daughter on a bus to school in the morning. "It was just a usual morning. She just smiled. When you saw her face, she told you everything. You don't need to listen to words from an angel," he said.
That afternoon Mr Konev got home to find the outer door of his flat open but the door to the living room jammed shut.
At first he thought Katerina was playing games but became increasingly alarmed when he could not open the door. Looking through the keyhole, he saw her schoolbag on the sofa and a man's black shoes.
Mr Konev ran back into the street and met the intruder face-to-face as he leapt from the window.
In broken English, he said: "He was crouched down, he was going to stand up. I saw him face on face, face on face. I said: 'What are you doing here?' He was just so calm, so cool, I can't believe.
"His eyes they didn't move, he was just looking at me, then he ran off down the street."
Mr Konev and his 31-year-old wife Zakalina, also a student, wept as they faced the press. He said the suspect, who was of Mediterranean or Eastern European appearance, had a splash of blood on his face. He chased him down the street and grabbed him but the man produced a knife, escaping on foot.
It was only when he returned to his flat that Mr Konev discovered his daughter lying injured. Katerina was later pronounced dead at hospital.
Mr Konev described how proud he and his wife were of her. "She was the best. At everything she was the best - at maths, music, at sport, she was perfect. She worked so hard. With friends she was so kind. All her friends loved her.
"She was just like an angel. She liked all people, doesn't matter where they were from. For her, the world was there to love," said Mr Konev.
Mr Konev appealed to the public to help catch his daughter's killer, warning that he was very dangerous and might kill again. "This is not a man, it can't be a man, it's a monster without feelings.
"To look in my face like that and be so cool, that's not a man. Animals don't kill like that, without reason. It's something I can't explain."
The detective leading the murder inquiry, Detective Superintendent Ken Woodward, said there was still no clear motive for the attack on the young girl.
There was no sign of a forced entry to the flat nor did anything appear to have been stolen. Nor did there appear to have been a sexual assault. Det Supt Woodward said: "We don't know why it happened."
Police issued a likeness of the suspect on Tuesday as well as a blurred closed-circuit television picture. The man they are looking for was described as between 45 and 50, around 5ft-5in tall and stockily built. He was balding, but still had dark hair, beginning to grey. He wore a light coloured jacket, an open-necked shirt, dark trousers and dark shoes. He carried a black canvas-type bag.
Mr Konev appealed to the public: "At the first chance, tell the police, inform the police, tell somebody. We don't know how many children he could kill if we don't catch him." Anyone with information should contact the murder incident room on 0181 246 0731.Reuse content