The Bill seeks to provide Indian citizenship to non-Muslims from Bangladesh, Pakistan and Afghanistan.
AGP president Atul Bora has written to BJP chief Amit Shah, saying the party will have no alternative but to "repudiate the existing alliance" in case of such an eventuality.
Steering BJP to power for the first time in the north east, Sarbananda Sonowal was sworn in as the 14th chief minister of Assam on May 24 heading a 11-member ministry that also included representatives of allies: AGP and Bodo Peoples Front (BPF).
The Congress stormed back to power in Assam for the third consecutive time securing an absolute majority by bagging 78 seats in the 126-member Assembly.