Justice R D Kothari posted the matter to July 16 after the actor's lawyer sought more time for representation of facts.
The high court had on June 27 initiated the final hearing on the actor's plea which he had filed in April 2008 seeking quashing of proceedings initiated against him and four others by the judicial magistrate of Bhuj district for alleged breach of the Wildlife (Protection) Act.
A complaint against Aamir and others was filed by the Forest Department for allegedly filming Chinkara in 'Lagaan' (2001) shooting for which was held mostly in Kutch in 2000.
As per the complaint, footage of Chinkara was taken without securing prior permission of the Forest Department.
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The judicial magistrate had in March 2008 issued bailable warrants against Aamir, his ex-wife Reena Dutta, director Ashutosh Gowarikar, executive director Srinivas Rao and cinematographer Ashok Mehta.
However, Aamir and others secured a stay from the high court on the warrants.
They had also contended that the forest department had obtained warrants against them in 2008 without hearing their side.
The forest department, which had initially closed the matter after conducting a preliminary inquiry, reopened the case after a fresh complaint was filed by an RTI activist Amit Jetha who was later shot dead in 2010.