Leaders of India's Congress have been holding talks with possible partners to form a coalition government after its shock victory in the general election.
Mrs Gandhi greets supporters outside her home
The party's own members will gather on Saturday to elect a parliamentary chief who would also become India's new prime minister in the Congress-led coalition.
Sonia Gandhi has refused to say if she wants to be the fourth member of the Nehru-Gandhi dynasty to hold the post.
India's stock markets fell on concerns of a possible Communist coalition role.
The Sensex index in Bombay closed 6.1% lower, its biggest daily decline in three years.
The fall reflected business concerns over Congress forming a coalition with left-wing allies which could be detrimental to India's privatisation programme.
Harkishan Singh Surjeet, of the Communist Party of India-Marxist - a key Congress ally - said the selling off of profit-making state-owned companies must stop.
'Reforms will continue'
But in her first post-election interview, Mrs Gandhi said India's economic reforms had been initiated by her husband, assassinated prime minister Rajiv Gandhi, and other Congress leaders and "naturally" would continue.
She again refused to be drawn on whether she wanted to follow her husband, his mother and his grandfather into the job of prime minister which many in her party believe is hers should she want it.
"I'm not attached to any particular position," she said.
"As far as the issue of prime minister, it will be the victorious members of parliament... who will elect the leader."
But she said she was pleased that her Italian heritage - which could make her the first foreign-born Indian prime minister - had not harmed Congress in the polls.
Hindu nationalists - and some Congress allies - say Mrs Gandhi is unacceptable as a leader for India as they view her as a foreigner.
"Most of the Congress Party's opponents used this against me, but I had full faith in the judgement of the people of my country," said Mrs Gandhi, who took Indian citizenship in 1983.
Congress, which led India to independence and then ran the country for most of the next 40 years, is returning to power after eight years in the doldrums.
Thousands of Congress supporters danced in the street outside Mrs Gandhi's home on Friday, singing, beating drums and showering her with petals when she made a brief appearance.
They shouted: "Sonia, we are with you!"
Congress won the most seats in the 545-member
parliament but the party fell short of a majority and is now in the process of looking for partners to enable it to rule.
As his defeat became clear, the outgoing Prime Minister Atal Behari Vajpayee said on national television that he accepted the verdict which was a demonstration of India's strong democratic roots.
"My party and alliance may have lost but India has won," he said.
He has been asked to continue until a new prime minister is sworn in.
The BBC's Adam Mynott in Delhi said it was the huge mass of Indians - largely ignored by the BJP and who had no electricity, poor sanitation and filthy water - who had spoken.
Mr Vajpayee called the poll six months early hoping to cash in on the peace initiative as well as an economic boom - but the move appears to have backfired.
Indians were still busy digesting the news on Friday.
Newspaper headlines reflected the disbelief as just days earlier the government was expected to come close to victory.
"Shock and Awesome," is the banner headline across the Hindustan Times
while The Times of India showed photographs of the Gandhi family under the headline: "King Cong, Queen Sonia".
Repolling has been ordered in three seats in the eastern state of Bihar because of irregularities and in one seat in Manipur because of a landslide. Two seats are appointed by the president.