The adjournment motion was moved by MLA and NC provincial president Nasir Aslam Wani seeking a discussion and reply of the state government on the arrest of Liyaqat.
However, Jammu and Kashmir National Panthers Party members stood up from their seats and opposed the adjournment motion saying they will not allow the House to discuss the issue.
Speaker Mubarak Gul rejected the motion saying Chief Minister Omar Abdullah has already taken up the matter with union Home Minister Sushilkumar Shinde and sought a probe into the affair by the National Investigation Agency.
Later, speaking to media outside the House, Wani said his party wanted to know whether Liyaqat had come under rehabilitation policy.
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"If he has come under this policy, there is no reason for him to be in jail. Chief Minister has taken up the issue with Union Home Minister, who had promised him probe," he said.
JKNPP Member Balwant Mankotia said, "Those who are involved in anti-India activities should not be discussed in the House. First they (NC) brought adjournment on Guru and now on Liyaqat. We will not allow this to happen".
The conflicting versions of Delhi Police and JK police over Shah's credentials are being examined by Ministry of Home Affairs after a row erupted.
The state government had entered into an unwritten understanding with the Centre that any youth who had joined militant ranks in 1990s and wished to return via Nepal would be allowed to do so provided he surrendered before Army or police in the Valley.