"We have raised our stake in the past two months through market purchases," R N Bhardwaj told Reuters.
He said the insurance monolith has the option of hiking its ownership to 20 per cent, which is the ceiling prescribed by the nation's insurance watchdog in individual companies.
L&T, India's No 2 cement maker, is in the midst of a takeover battle. Last week a tribunal upheld the market regulator's ruling asking rival Grasim Industries to put on hold a plan to buy a further 20 per cent in L&T.
Financial institutions, led by LIC, have opposed Grasim's offer made at Rs 190 per share saying the price was not attractive.
Since then, the institutions, which own about 39 per cent in L&T, have been looking to hike their holding as it would boost their bargaining power.
Last month, the Securities and Exchange Board of India asked Grasim to delay its offer until it had finished investigating a possible violation of takeover rules by Grasim. It also barred Grasim from acquiring more shares until further notice.
L&T shares were up 0.64 per cent at Rs 196.90 while Grasim shares were down 0.12 per cent at Rs 295 on the Bombay Stock Exchange, whose key index ended provisionally up 0.62 per cent.