A Bangladesh Supreme Court judge, acting on a last-minute appeal from attorneys for Mollah, ordered the stay only 90 minutes before the man was to be hanged, the Bangladesh Daily Star reported.
CNN reported two U.N. human rights experts had earlier urged the hanging be halted, saying Mollah's trial may not have been fair.
The Star said jail authorities had completed all preparations for the execution two days after the death sentence was issued for Mollah, accused of war crimes during Bangladesh's 1971 war of independence from Pakistan. He had denied the charges.
State Minister for Law Qamrul Islam told the Star the government would move the apex court to vacate the stay order. The hearing on the review petition was set for Wednesday morning before the appellate division of the Supreme Court.
Mollah had been assistant secretary general of the now banned Jamaat-e-Islami party and his sentencing by a tribunal set up by the government had sparked rioting in the streets, CNN reported.
He was previously given a life sentence but the Supreme Court gave him the death penalty.
The brutal 1971 independence war from which Bangladesh emerged as an independent country, however, resulted in the deaths of hundreds of thousands of people and left deep scars in the minds of the Bangladeshis. Mollah was accused of being part of a group that did not want to split from Pakistan and aided the Pakistani military's crackdown.