Malaysia’s Negeri Sembilan state was pushed deeper into crisis after Barisan Nasional (BN), a key ally in Prime Minister Anwar Ibrahim’s coalition government, declared it had secured a simple majority to form a new state administration with the opposition.

The move turns an extraordinary palace dispute into the sharpest state-level test yet of Anwar’s fragile ruling alliance, ahead of a national poll due in less than two years.

BN, the former ruling coalition led by Umno that ruled Malaysia for...