Indian shares have recorded their biggest-ever fall in a single day's trading amid fears the new government could stall economic reform.
Mrs Gandhi is expected to be sworn in within days
The Bombay Stock Exchange at one point plummeted more than 700 points, a 15% drop, before recovering slightly to finish down 11.1% or 564.71 points.
Traders have fears about the economic plans of the new left-leaning Congress government, to be led by Sonia Gandhi.
Yet Communist parties said they will back, but not join the government.
Without an outright majority, the Congress party needs the support of such fringe left-wing groups, which are in turn scaring investors who fear they will put the breaks on India's privatisation programme and other market liberalisations.
The Communist Party of India (Marxist), the biggest left-wing party, said it took "a collective decision" to stay out of government after a two-hour meeting of its central committee.
Sonia Gandhi is now due to meet the president on Tuesday to formally stake her claim to form a government, with Congress saying she will be sworn in as the new prime minister on Wednesday.
Monday's fall on the Bombay Stock Exchange (BSE) 30-share sensitive index started almost immediately, with it losing 553.29 points in the first few minutes of trading, falling below the psychologically important 5,000-point mark and wiping billions of dollars off the value of India's listed companies.
Trading was temporarily suspended, but the index slid a further 200 points after it resumed, forcing a second suspension.
The BSE sensitive index closed the day at 4,505.87 points, down 11%.
Analysts say the market crashed after foreign institutional investors, who had invested some $10bn in the Indian stock markets over the past year, began to sell heavily.
"Their expectations from India were very high," market analyst Debashis Basu told BBC News Online.
"Now they are jittery about the new government's direction on reforms and are pulling out."
Congress Party officials played down the fears.
"I wish to assure the investing community our policies will be pro-growth and pro-savings," senior Congress leader and former finance minister Manmohan Singh told the BBC.
"We are not going to reverse the good work that was done in the past 10-12 years," he said.
Mr Singh, who launched India's economic reforms under a Congress government in the 1990s, warned that the government would take action against speculators seeking to manipulate stock prices.
"The new government will not hesitate to take action against those who seek to manipulate the market and create artificial panic," Mr Singh said.
Members of the outgoing Bharatiya Janata Party (BJP) were somewhat mixed in their opinions on why the Indian stock market fell so heavily.
Arun Jaitley, a senior BJP leader and former commerce minister, said the chaos on the market was due to "certain outlandish statements by leaders of left parties".
"The BJP believes that governance is very serious business," he said.
Yet Ashok Lahiri, the outgoing government's chief economic adviser, told investors there was "no reason for panic" as the
economy's fundamentals were "very strong".