(Reuters) - The BSE Sensex and Nifty slumped more than 3 percent on Tuesday, posting their biggest daily loss since the rupee crisis in 2013 as a continued slide in oil prices hit emerging markets, sending blue-chips such as State Bank of India sharply lower.

The BSE Sensex declined 3.07 percent and the broader Nifty 3 percent, their biggest daily percentage fall since Sept. 3, 2013, when the rupee was still reeling from its worst market turmoil since the 1991 balance of payment crisis.

Analysts say domestic shares could be vulnerable to falls, with the Nifty having gained 31.4 percent in 2014, its best gain since 2009, although they say hopes about an economic recovery and fiscal reforms could prevent excessive declines.

Whether foreign investors retreat will be key after they bought a net $16.1 billion last year.

"This fall is largely attributed to global factors including crude. I admit that it's a sharp correction, but it will throw more opportunities for fresh money to come in," said Deven Choksey, managing director, KR CHoksey Securities.

Blue-chips led losses as global shares sank on the back of a continued slide in oil prices that is raising concerns about the health of the global economy. ICICI Bank lost 4.2 percent, State Bank of India fell 4.1 percent while Infosys fell 2.1 percent.

Oil explorers declined, tracking the fall in U.S. crude oil prices. Reliance Industries fell 4.5 percent, while Oil and Natural Gas Corp slumped 5.7 percent.