Leader of Opposition in Legislative Council Sushil Kumar Modi told reporters that police firing on people reflected poor law and order situation in the state under JD(U) government.
He demanded a judicial inquiry into the incident.
Sushil Modi said that the incident triggered by exchange of "objectionable" MMS by two friends of different communities on Monday was a fallout of "lapse" on part of district administration.
"The District Magistrate and Superintendent of Police reached the site a good eight hours after the firing in which two persons were killed," he said and assailed "partisan" approach of police in the incident.
Sushil Modi said a party fact-finding team would visit Akbarpur village of Rohtas district where firing took place yesterday in which Pradeep Paswan and Upendra Kushwaha lost their lives and nine others, including two policemen, were injured.
His counterpart in the Assembly, Nand Kishore Yadav raised question on police opening fire on a group of people who had gone to enquire about whereabouts of one Ajay Kumar involved in exchange of MMS, who was arrested by the police and transferred to another police station whose location it refused to disclose to his family.
"One of the victims received bullet wounds near the ear and another in the stomach which shows that standard practise of firing below waist was not followed by the police," Sushil Modi and Yadav said.
BJP members trooped into the well in both the Houses of Bihar Legislature when their adjournment notice on the subject was not entertained.
Chief Minister Jitan Ram Manjhi however, justified police firing and turned down the BJP demand for judicial probe.
"Police had to open fire in its defence as rampaging mob indulged in vandalism and looted rifles from police station," Manjhi told reporters in his Assembly chamber.
He said Inspector General of Police of Patna zone and Commissioners have been camping at the incident site and probing the matter. "So what is the need for judicial or other inquiry?" he said in reply to a question on BJP demand for judicial probe.
Sushil Modi criticised the CM for justifying the police firing even before a probe report has been filed into the incident.
The BJP leaders demanded Rs 10 lakh compensation for the family of the two victims.
Sushil Modi said a call for Rohtas bandh has been given for tomorrow. The bandh would be till 3 pm so that Muslims do not face problem in ending their Ramzan fast in the evening.