India’s biggest life insurer stumbled on its trading debut after leaning on small investors to help it push through a record $2.7 billion IPO despite global market turbulence.

The disappointing first-day performance for state-owned Life Insurance Corp. of India came even after New Delhi had slashed the size and valuation of the share sale in response to choppy markets.

The scaled-back deal, in which the government sold a 3.5% stake, was still India’s largest-ever initial public offering. It was also the third-biggest in the world this year, according to Dealogic data, amid an international slowdown in companies going public.

LIC closed at 874.45 Indian rupees per share Tuesday, the equivalent of $11.25, falling despite a broader market rally. The closing price was 7.8% below the IPO price of 949 rupees.

While investors overall placed orders for nearly three times the shares on offer, demand was strongest from individuals, who were offered large incentives to take part. LIC offered employees and other individual investors a 4.7% discount to the offer price and gave policyholders a 6.3% markdown.

Demand from foreign investors, who had been huge buyers in an IPO boom last year, was muted. They bid for just 61% of the total shares reserved for institutional buyers.

Foreigners have been net sellers of Indian shares every month since October, pulling out more than $25 billion through Tuesday, amid uncertainties caused by Russia’s invasion of Ukraine, quickening inflation and higher interest rates globally. Rising oil prices are pushing up India’s import bill and pressuring the rupee.

India’s flagship S&P BSE Sensex index rose 2.5% Tuesday. It is down about 6.8% this year, according to FactSet, a more resilient performance than many other major indexes.

Earlier this month, India’s central bank abruptly raised benchmark interest rates by 0.4 percentage point, citing inflationary pressures and the risks that emerging markets face as rich countries withdraw their easy-money policies. India’s consumer-price index rose 7.8% in April compared with a year earlier, above the central bank’s 2% to 6% target range.

The previous holder of the record for India’s largest IPO also fared poorly in the public markets. Shares in One97 Communications Ltd. , the parent of the financial-technology platform Paytm, fell 27% on their first day of trading last November. On Tuesday, One97 shares closed nearly 73% below their issue price.

With a market value of about 5.5 trillion rupees, or $71 billion, LIC is now the fifth-most valuable company listed on the exchange operated by Mumbai’s BSE Ltd., according to BSE data.

Some investors had high hopes for LIC’s share listing, as it is a household name in India, with around 280 million policies.

In recent months, brokers like Chandra Bhan Singh, who heads a branch for

Geojit Financial Services in the north Indian city of Bareilly, had been persuading LIC policyholders to become shareholders. Many of them had never invested in stocks. On Tuesday, Mr. Singh said he got calls from some owners of LIC shares asking what to do now that the shares were falling.

“We’re telling them that if you can buy, then buy more,” he said. Like many fund managers and brokers in India, Mr. Singh attributed the decline in LIC’s share price to weaker global markets, and he said he believes the stock has merit.

Some analysts said Tuesday’s selling was partly driven by smaller investors, including regular individuals and richer buyers, who had bought LIC stock in the hope of selling it quickly at a profit. After the stock failed to trade up on its debut, these holders were exiting to limit their losses.

“They didn’t get anything,” said Atul Sharedalal, director of Pravin Ratilal Share and Stock Brokers Ltd., in the city of Ahmedabad. But he said he was hopeful the stock would recover. “Let’s see one-two months later,” he said.

Write to Shefali Anand at shefali.anand@wsj.com