The decision came hours after UN High Commissioner for Human Rights Louise Arbour called on Iran to stay the executions "in strict compliance with [Iran's] international human rights obligations."
Behnoud Shojaie and Mohammad Fedaie were among the four condemned men named by Arbour. The fates of the other two men, Said Jazie and Behnam Zareh, remain unclear.
In a statement, the office of the head of the Iranian judiciary, Ayatollah Mahmud Hashemi Shahrudi, said the stay of execution was decided in order "to reach an agreement with the victims' families."
Under Islamic Shari'a law, a victim's family can spare a murderer from execution by accepting financial compensation -- so-called blood money. In such cases, the convict pays the money and serves only a prison sentence.
Iranian media reported that Shojaie and Fedaie were believed to have been among 11 convicts to be hanged within Tehran's notorious Evin prison on June 11. Mohammad Mostafai, the two young convicts' lawyer, tells Radio Farda that human rights groups have been putting pressure on Iran to stay their execution.
"We have been writing letters to point out there were doubts and problems in those criminal cases," Mostafai says. "In addition, many human rights activists tried very hard to somehow prevent the executions."
In Iran, murder, adultery, drug trafficking, rape, armed robbery, and apostasy are all punishable by death. In recent years, human rights activists have criticized Iran's growing use of the death penalty, particularly against juvenile offenders.
London-based Amnesty International has listed Iran as the second-most-prolific executioner in the world, with some 317 people put to death last year, after China, which reportedly carried out 470 death sentences.
Iranian officials counter that the country is not violating human rights and accuse the West of double standards.
International rights groups and feminist campaigners inside Iran have also called on Tehran to raise the age of legal responsibility, which deems a girl punishable from the age of 9 and a boy from the age of 15.
Radio Farda correspondent Farin Assemi contributed to this report