Clashes broke out at the function of Hurriyat Conference at Rajbagh headquarters as Shah and his supporters lamented that no explanation was sought from Bhat for violating the Hurriyat constitution, sources in the amalgam said.
They said the rival supporters hurled furniture at each other, but none was injured in the clashes.
Bhat, earlier this month, had said the United Nations resolutions on Kashmir were not practicable in the present geo-political scenario.
The statement had drawn widespread criticism within and outside the moderate amalgam as Bhat was accused of preparing for contesting the 2014 Assembly elections.
Shah said it was strange that the issue has not been even discussed within the forum. He was expelled from Hurriyat in 2002 for holding talks with K C Pant in violation of the Hurriyat whip. Shah was later reinstated in 2008.
Former Hurriyat Chairman Maulana Abbas Ansari sought to play down the clashes, saying such incidents take place in every democratic institution.
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"Such things happen in the assembly and parliament also but that does not bring it down. However, the Hurriyat leaders should not take internal differences to public domain," Ansari said.
Hurriyat Chairman Mirwaiz Umar Farooq was not present at the function as he is placed under house arrest.
Hurriyat is observing "martyrdom week" to commemorate the 21st death anniversary of Maulana Mohammad Farooq and 10th death anniversary of Abdul Gani Lone. Both the separatist leaders were killed by militants.