The 25-year-old is in an induced coma after collapsing in the ring at Wembley Arena following a 10th-round stoppage.
The ringside doctor made the call due to swelling above the left eye of Blackwell, who was carried out of the stadium on a stretcher.
It has now emerged that Chris Eubank Jr's father urged his son to target Blackwell's body rather than his head because he was concerned that the opponent would end up hurt.
According to Sky Sports News, at the end of the eighth round, Eubank entered the ring and said: "If he doesn't stop it and we keep beating him like this, one, he is getting hurt, and two, if it goes to a decision - why didn't the referee stop the fight? I don't get why.
"So maybe you shouldn't leave it to the referee. You're not going to take him out to the face, you're going to take him out to the body."
TV cameras also picked up footage of the former world champion banging on the floor of the ring trying to get referee Victor Loughlin to stop the fight.