About 150 people, mostly students, were killed when heavily-armed militants attacked the army run school in the northwestern city of Peshawar in December.
A military court in August sentenced seven militants to death for their involvement in the attack. The militants were arrested for facilitating the massacre.
The Prime Minister's Office in a statement said that four convicted men filed mercy appeals to the President which is the last forum against death sentence.
The Prime Minister has "advised the President to reject the mercy petitions of all four convicted terrorists of Army Public School Peshawar terrorist attack," said the statement.
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"The brutal and merciless killings of our children convinced us that the perpetrators of such crimes do not deserve any mercy," it said.
It also said that immediately after the school tragedy, the state, the elected representatives, all political parties and all state institution unanimously decided to bring the perpetrators of the crime to justice.
He said that the government set up Military Courts after the attack to bring the perpetrators of most heinous crimes to justice in a short span of time.
After rejection of mercy appeals, there will be no legal bar to hang the convicts.
Pakistan has lifted moratorium on the hangings and close to 300 convicts have been hanged since the school attack.