Several seniors across factions are understood to be backing Venugopal internally, arguing that the CM should be selected through organisational consensus rather than public pressure.
VCK chief Thol Thirumavalavan has already announced that his party's decision would align with the decision of the Left parties, which extended support to TVK on Friday.
Governor RN Ravi administered the oath of office to Adhikari at a grand ceremony held at Kolkata's Brigade Parade Grounds in the presence of Prime Minister Narendra Modi and several Union ministers.