The Indian government is again looking to sell its majority stake in the country’s biggest shipping company, but may face the same headwinds that have blocked past privatization efforts.

The Shipping Corp. of India is at the heart of the country’s industrial economy, with about 70 cargo vessels of all types worth some $1.2 billion. That makes it a key target for Prime Minister Narendra Modi’s bid to sell off state assets.

“A proposal to divest the state’s 63.8% holding has been submitted to the cabinet which will decide later this month,” said a ministry of shipping official, who spoke on condition of anonymity because he wasn’t authorized to speak with the media. “It’s part of a wider move to privatize a number of state assets.”

Newsletter Sign-up The Logistics Report Top news and in-depth analysis on the world of logistics, from supply chain to transport and technology. PREVIEW

SCI operates close to a third of all Indian waterborne tonnage, with five very large crude carriers and 29 smaller crude tankers, product tankers and gas carriers. Its fleet also includes dry bulk carriers, container ships and ferries.

The government first tried to sell its stake in 2017 but the sale was canceled after pushback by various bodies, including the ministry of shipping. Privatizations in India are often complicated, with a number of senior politicians standing steadfast against the sale of what they describe as vital national assets.

Mr. Modi’s government has been pushing to sell government stakes in dozens of Central Public-Sector Enterprises or Undertakings, CPSEs, as part of what it calls “investor-friendly reform” across many parts of the economy including railways, shipping, banking, mining, petrochemicals and airlines.

Although many economists believe the majority of India’s more than 300 CPSEs can be privatized, public-sector jobs are highly sought-after in India because they offer relatively secure employment and better-than-average salaries and working conditions.

In a 2018 jobs competition, around 25 million people applied for 90,000 positions at the country’s giant state-run railways, according to government data.

The Mumbai-based Shipping Corp. of India, which is listed on the local bourse, has a market value of around $290 million. Apart from ships it also owns premium property in Mumbai, including its 19-storey headquarters.

Opponents of the sale say a good part of India’s vital oil imports move on SCI ships and selling the carrier could rattle oil supplies.

Company executives say the biggest hurdle to the sale will be trying to sell a company with so many ship types, however. Private-sector operators may view such spread across various markets as inefficient.

“There are few shipping operators or other investors that are looking to invest in so many ship types,” the shipping ministry executive said. “It could be broken up and then sold, but this will take years and face a lot of opposition.”

Write to Costas Paris at costas.paris@wsj.com