Asked about the incident while on a trip to Brussels, Prime Minister Sir Keir Starmer said his first thoughts "as a father" were with the victim's family.
"The terrible stabbing in Sheffield is one where I think the whole country would want to reach out to the family, to the friends, to the school, the entire community in their grief and mourn with them," he said.
Louise Haigh, the MP for Sheffield Heeley, said the news was "horrific" and that "serious questions" would have to be answered about how it could have happened.
Anti-knife crime campaigners in the area have said incidents like this should not happen.
Amaan Ahmed, who manages the Castle Asian Community Trust near the school, said he feared the boy's death would leave parents wondering if they should send their children back to school.
"If it can happen in a public place like a school, people will be worried about going to the park I think too," he added.
Sheffield-based Anthony Olaseinde, who works for the charity Always an Alternative, said the incident was "heart-breaking".
"Something like this should not happen," he said.
He said the charity had held sessions at All Saints and worked with young people at the school.