The regulator will check how insurers set and change actuarial assumptions before new rules on those assumptions are due to take effect on 1 January 2027.
The name change, which took effect on 22 September, follows efforts by UK-based joint venture partner Prudential to transition from promoter to investor status in the insurer.
The reported bid follows a series of LIC investments across India's financial sector, including moves to increase its holdings in ICICI Bank and HDFC Bank.
The move removes the requirement for prior regulatory approval to repatriate dividends and aligns intermediary rules with India's revised insurance and foreign investment framework.
The cases have drawn attention to K-SURE's buyer-screening processes, with lawmakers urging a reassessment of underwriting standards and coverage approval practices.
Insurance-linked securities, captives and other alternative capital structures are increasingly important tools for supporting Asia's rising infrastructure risk exposures, the regulator said.