Supreme Court lawyer Advocate Eunus Ali Akond who filed the writ said it will be placed before another bench on Monday for hearing.
He said the prime accused in the murder case is still at large although four days have elapsed since the brutal murder.
Home and law secretaries, Inspector General of Police and Director General of Rapid Action Battalion (Rab) have been made respondents to the writ petition.
Rifat Sharif, 22, was hacked to death by criminals in front of his wife in broad daylight in Barguna district town on Wednesday. The incident was caught on surveillance camera.
Rifat’s father Dulal Sharif had filed a case against 12 named and 5-7 unnamed people after the murder.
Six people, including two FIR-named accused, have so far been arrested over the murder.
Police on Thursday issued red alert at all international airports, river ports and land ports across Bangladesh so that the killers cannot flee the country.