"Its a welcome step which was desired for long," Kumar told reporters emerging from a meeting of the cabinet here.
His former NDA partner BJP has opposed the Bill with its prime ministerial candidate Narendra Modi describing it as "recipe for disaster."
Kumar, who is the driving force of the JD(U), insisted on political dialogue with the states before giving it shape of a law.
The Bihar Chief Minister said there were talks for such a legislation for several years and many drafts were made, but nothing concrete happened.
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"Now that the Prevention of Communal and Targeted Violence (Accessto Justice and Reparations) Bill, 2013, has been cleared by the Union Cabinet for introduction in the Parliament, its a desired step," he said.
Highlighting the seriousness of his government towards riots victims, he said after coming to power in 2005, a commission was set up in 2006 on the 1990 communal violence in Bhagalpur.
Many cases were reopened and chargesheet submitted in the courts to nail the culprits, he said.
For victims of Bhagalpur riots, the Bihar government doubled the life long pension to Rs 5000 a month recently, Kumar added.