The meeting is the first in India for the directors of the investment bank.
Access to the presidential suite hired by Goldman Sachs at Mumbai's landmark Taj Mahal Palace hotel, which was heavily damaged during the deadly November 2008 militant attack on the financial capital, was blocked to non-guests on Thursday morning.
Goldman declined to give any details of the annual board meeting, but a source previously told Reuters the U.S. bank had scheduled it in India in a sign of its "commitment" to the fast-growing emerging market.
Officials including Blankfein, Chief Operating Officer Gary Cohn and board members including ArcelorMittal Chief Executive Lakshmi Mittal were in India for a series of meetings, including a dinner on Thursday night with top Indian industrialists.
They were due to travel later to the capital, New Delhi, people familiar with the matter said.
The Taj hotel overlooks Mumbai's bustling harbour and the Gateway of India arch, and hosted U.S. President Barack Obama on his visit in November 2010.
Goldman Sachs, long Wall Street's pre-eminent investment bank, has become a lightning rod for criticism of the financial industry in the aftermath of the global financial crisis.
The unwelcome spotlight was trained on it again when a mid-level executive resigned and fired off a blistering attack on the firm in a New York Times op-ed on March 14, describing a "toxic and destructive" culture motivated by greed.
Greg Smith's scathing remarks have prompted an outpouring of criticism, ridicule - and defence - of Goldman.
Proposals to separate the CEO and chairman roles have long been sought by outside groups, but two people familiar with management thinking provided the first indication that internal discussions about such a move have taken place.
Under such a restructuring, Cohn would assume the chief executive officer role and Vice Chairman J. Michael Evans would become president, leaving Blankfein with only the chairman role, two sources told Reuters this week.
With its big potential but low fees and fierce competition, India has proven a tough m arket for global investment banks, including Goldman, whose business in India includes fixed income, economic and investment research and offshore asset management services, as well as investment banking.
Last year it ranked second in the completed mergers and acquisitions advisory league table for India, while it ranked ninth in equity capital markets business.
The bank, which in January reported a 56 percent drop in fourth-quarter profit, said in its 2010 annual report it has seen higher revenue contribution from its "growth markets" such as China and Brazil and that it has "much more room" to grow. (Additional reporting by Nandita Bose in MUMBAI and Lawrence White in HONG KONG; Writing by Sumeet Chatterjee; Editing by Tony Munroe and Alex Richardson)
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