India's biggest-ever IPO, state-owned insurance giant LIC, fell seven percent from its flotation price of 949 rupees when it made its market debut Tuesday.

The government raised $2.7 billion from the sale of 3.5 percent of its stake in Life Insurance Corporation of India as it seeks to fix tattered public finances.

The flotation, delayed from March due to market volatility and cut back in the face of limited demand, was oversubscribed nearly three times during the six-day application period.

The muted debut could test the patience of new shareholders as Prime Minister Narendra Modi seeks to sell off state assets to "monetise and modernise" nationalised companies and plug an estimated 16.6 trillion rupee ($213.5 billion) fiscal deficit.

Shares in LIC listed at a seven percent discount from its offer price of 949 rupees, before climbing slightly -- though it remained well below the flotation price.

Founded in 1956 by nationalising and combining more than 240 firms, LIC was for decades synonymous with life insurance in post-independence India, until the entry of private companies in 2000.

It continues to lead the pack with a 61 percent share of the market in India, with its army of 1.3 million "LIC agents" giving it huge reach, particularly in remote rural areas.

But LIC's market share has declined steadily in the face of competition from net-savvy private insurers offering specialised products.