The JDU and RJD had come together ending years of acrimony and formed the government in Bihar last month.
A senior RJD leader has blamed Bihar Chief Minister Nitish Kumar for rising incidents of crime in the state. Party vice president Raghubansh Prasad Singh today said it is for Mr Kumar to check the slide.
Mr Kumar's JDU and the RJD together formed the government in Bihar after a landslide in November, ending years of political rivalry. The JDU had paired up with the BJP a decade ago to defeat the RJD and end its 15-year-rule in Bihar.
In the last week alone, three engineers were murdered in two separate incidents and a businessman shot dead leading to criticism of the coalition government.
"Sensational murders of engineers in Bihar recently have proved that law and order is not good in the state," Mr Singh said, the news agency Press Trust of India reported. "Nitish Kumar, who is sitting on the driver's seat of the government, should initiate stern measures to check further slide."
The RJD leader said his party "is sitting on the back seat and its prime duty of man on the wheel to drive the vehicle (the coalition government) safely." Mr Kumar holds the Home portfolio in the state.
Mr Singh said, "JD(U) people are in the habit of hearing 'jay kaar' (praise) which they should end and take strong measures to rein in crime causing disturbance to people."
He backed his party chief Lalu Prasad Yadav, whose two sons are ministers in the government, for speaking out against rising crimes in the state.
Senior JD(U) leader and former minister Shyam Rajak hit back at the RJD saying it was Mr Kumar who had pulled Bihar out of perceived lawlessness and hence, needed no advise on the law and order situation. The period from 1990 to 2005, when the RJD was in power, is often described by the opposition as the days of the law of the jungle
"Even a child can give advice," he said, in an apparent dig at the RJD.
The Congress backed Mr Kumar. "Law and order has always been the USP of Nitish Kumar for which he has won praise across the country. Some criminal incidents have taken place to which the CM is looking into and will handle it," Bihar Education Minister Ashok Choudhary, who is also state Congress chief, said. The Congress is the third partner in the coalition.