A bench of Chief Justice G Rohini and Justice Sangita Dhingra Sehgaldirected the ministries concerned of both the governments to file an affidavit by May 9.
During the proceedings, the court was informed that an identical issue is pending before the Supreme Court.
The respondents sought dismissal of the public interest litigation (PIL) which sought directions to the authorities concerned to address the issue.
Taking note of which, the bench said the government should also put this fact in their affidavit.
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The plea has alleged that the Centre, the Delhi government and the Animal Welfare Board of India (AWBI) are turning a blind eye to the violations and has soughtdirections to them to issue guidelines to address the issue.
The plea moved by two animal rights activists -- Saurabh Gupta and Gaurav Gupta -- have alleged that the trucks are filled three to six times beyond the legal limit and as a result 50 per cent of more ofsuch cattle die during every trip.
They have sought issuance of guidelines to be followed by police in such cases.
The petition, filed through advocate Anupam Tripathi, hasalso sought setting up of raiding teams to prevent and curb illegal transport of cattle.