* Country's biggest pension fund to halt stock trade with Samsung
* Shares have plunged 10 pct since Friday's fat finger error
* Public outcry over employees who sold stocks mistakenly given (Recasts and adds comment from regulator, analyst)
SEOUL, April 10 (Reuters) - Samsung Securities Co Ltd's woes deepened on Tuesday as South Korea's biggest pension fund stopped using the broker to trade stocks in the wake of a 'fat finger' error that has prompted a huge public outcry and calls for change in the industry.
Anger over the accidental issuance of 2.8 billion shares to employees - more than 30 times the number of its outstanding shares and theoretically worth some $100 billion, has only gained momentum after it was discovered that 16 workers quickly sold off shares.
Authorities have launched an investigation into Samsung Securities, the country's fourth biggest broker by market value, as well as into the stock trading across the sector.
"Samsung should quickly recognize this situation as a crisis. This is not just a problem of 16 employees, it is a company and industry wide issue," said Kim Tae-gi, an economics professor at Dankook University.
The company issued the shares in error on Friday when it was supposed to pay dividends worth 2.8 billion won to employees under a stock ownership plan, with a worker entering 'shares' instead of 'won' into a computer.
It took the firm 37 minutes to realize the error and halt trading by its employees. During that time, some employees sold off the stocks mistakenly given, ignoring warnings from the company, the Financial Supervisory Service said.
Since then, Samsung Securities stock has lost 10 percent, wiping about $330 million from its market value.
An official with the National Pension Service, the world's third-biggest pension fund, declined to disclose the volume of the fund's stock trading done through Samsung. It had 136 trillion won ($127 billion) of its assets invested in the local stock market as of January.
The fund will continue to outsource fund management to Samsung until regulators announce results of the ongoing investigation, the official added.
Financial Supervisory Service Governor Kim Ki-sik urged domestic brokerages on Tuesday to strengthen their internal control systems and work to rebuild investor trust, saying the error was a massive shock but also an opportunity to build a solid trading environment.
Over the last three days, more than a 200,000 people have signed a petition on the presidential Blue House's website, calling for employees who sold off the shares to be severely punished.
($1 = 1,070.7000 won) (Reporting by Joyce Lee and Ju-min Park; Additional reporting by Dahee Kim; Editing by Edwina Gibbs)