Speaking to her party in the central hall of Parliament, she said she would "humbly decline" to be the next prime minister of the world's largest democracy.
"The post of prime minister has not been my aim," she said over a crowd that yelled at her to take the job. "I was always certain that if ever I found myself in the position I am in today I would follow my inner voice. I humbly decline the post."
Gandhi's Congress party and allies trounced the Hindu-nationalist party of caretaker Prime Minister Atal Bihari Vajpayee and his Democratic National Alliance in national elections that ended last week.
The new Congress lawmakers shouted and pleaded with her to change her mind, and she had to stop several times to get the audience to quiet down.
"I request you to accept my decision," the Italian-born Gandhi, 52, said, adding that she would not reconsider.
The announcement in the massive, colonial-era building was attended by 145 newly elected lamwakers from her Congress party and her children Rahul and Priayanka.
"It is my inner voice, my conscience," she said. "My responsibility at this critical time is to provide India with a secular government that is strong and stable."
Financial markets soared before the announcement just on speculation that someone else would lead the country following last week's electoral upset of Prime Minister Atal Bihari Vajpayee National Democratic Alliance coalition.
"There are rumors that her children are against her becoming prime minister, maybe because of security reasons," Somnath Chatterjee, an elected Parliament member from the Communist Party of India-Marxist, said before the announcement.
"We worked so hard under her leadership. If she does not become the PM, our whole cause is lost," Salman Khursheed, a senior Congress leader, said. "This is something that the Congress workers will go to any lengths to change."
Congress sources said Gandhi was forwarding the names of Manmohan Singh and Pranab Kumar Mukerjee, both of whom were Congress finance ministers. Singh was the architect of India's economic liberalization program, and many believe he would be able to strike a balance between demands for leftists and policies that benefit businesses.
The reports that Gandhi might not accept the leadership post prompted India's stock market to soar Tuesday.
The benchmark index of the Bombay Stock Exchange, the Sensex, ended up 8.6 percent to provisionally close at 4893.64 points, a day after the biggest one-day dive in its 129-year history.
The new Parliament must sit by Aug. 6, six months from the day that the previous legislature was dissolved.
The Congress party and its allies did not win an outright majority in Parliament in the six-week elections that ended last week, but the two communist parties have said they would support her bid to become prime minister.
Investors feared Gandhi might have backtracked on her pledge to go forward with economic liberalization, or that the Communists, with 62 seats in the 545-member parliament, could block key reforms such as the privatization of state-run companies.
The two communist parties — the Communist Party of India and the Communist Party of India-Marxist — announced Monday they would back Gandhi's ascension as prime minister but would stay out of the coalition until they were able to review the positions of the new 11-member Congress alliance.
Gandhi needed the leftist parties because even with the announced backing Monday of the socialist Samajwadi Party, the Congress would have only 257 seats, short of the 272 it needs for a majority among the 543 elected seats of the lower house of Parliament, the Lok Sabha.
The Gandhi dynasty dominated Indian politics since independence from British colonial rule in 1947. Jawaharlal Nehru, India's first prime minister, headed the country from independence until his 1964 death. He was followed by his daughter, Indira Gandhi, who was killed by her own bodyguards in 1984.
Rajiv, her son and Sonia's husband, took power and ruled until 1989. Two years later, he too was assassinated.
The family is not related to Mohandas Gandhi, India's independence leader.