"Sensational murders of engineers in Bihar recently have proved that law and order is not good in the state," Singh told PTI.
Expressing concern over spurt in crime, Singh, who is vice-president of RJD, said it was the responsibility of the state government to maintain law and order.
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Singh, who is a former Union minister, said, "Nitish Kumar, who is sitting on the driver's seat of the government, should initiate stern measures to check further slide."
He said the RJD "is sitting on the back seat and its prime duty of man on the wheel to drive the vehicle (coalition government) safely."
In a comment which may not go down well with ally JD(U), Singh said, "JD(U) people are in the habit of hearing 'jay kaar' (hailing words) which they should end and take strong measures to rein in crime causing disturbance to people."
Singh said the RJD chief has rightly spoken about crime situation in Bihar and sought action in accordance with it.
Senior JD(U) leader and former minister Shyam Rajak said Kumar has the track record of pulling Bihar out of bad days and, hence, needed no advise on law and order situation.
"Even a child can give advice," he said apparently reacting to Singh's views.
JD(U) spokesman Neeraj Kumar said, "11 crore citizens of Bihar did 'jay kaara' of Nitish Kumar in poll and gave three-fourth seats to the coalition headed by Kumar."
Meanwhile, Congress, a partner in the coalition government in Bihar, came in support of 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, told PTI.
He took potshots at BJP for making adverse comments on the government in the wake of killing of engineers in Darbhanga and a few other murders.
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"BJP had given slogan of 'jungle raj-2' in the poll which people of Bihar have thoroughly rejected by voting coalition government to power with thumping majority," Choudhary said.
Opposition BJP lapped up the situation in the wake of the crime spurt to attack the Nitish Kumar government.
Senior BJP leader Nand Kishore Yadav said that the Nitish Kumar government appears to have lost 'ekbaal' (wherewithal) due to which criminals were feeling brave.
"The war of words between RJD and JD(U) has proved that there was no cohesion in the coalition government which has been speaking a lot on controlling crime but nothing is visible on the ground so far," Yadav said.
Senior BJP leader and former Union minister C P Thakur today met Governor Ram Nath Kovind and drew his attention towards spate of crime incidents in Bihar in recent days.
Faced with the charge of return of 'jungle raj' in Bihar amid the spurt in crime in the state, Lalu Prasad had on Tuesday said those who had challenged law and order during his rule were doing it again.
He blamed former state police chief (Abhyanand) for the demolishing morale of police force in the wake of killing of Ranvir Sena, a private militia of upper caste landlords, Brahmeshwar Mukhiya. Abhyanand had served as police chief for long under Nitish Kumar before retirement recently.