Gandhi's hopes to lead India's next government were set back when Mulayam Singh Yadav, head of the Socialist Party, said he would not support any of the major blocs trying to cobble together a new government. The party controls 20 of the 543 seats in parliament.
There remained an outside chance that non-Congress parties would try to form a coalition, or that the Bharatiya Janata Party, whose coalition lost a confidence vote a week ago, would seek the president's approval to try again.
If no one succeeds in forming a government, India would face its third election in three years - a prospect both Congress and the BJP say they want to avoid.
Congress did not immediately concede defeat, though party workers milled around dejectedly at Gandhi's home when the radio reported the decision.
Earlier, leaders of two leftist parties that control seven parliament seats told the president they would not support a Congress government, while the leader of a five-seat party representing lower castes said the party preferred elections to choosing between Congress and the BJP.
Gandhi had promised to show President K.R. Narayanan by Friday that she was supported by 272 members of the 543-seat legislature.
"Both BJP and Congress are responsible for the poor state of the country," Yadav said in a written statement issued after his meeting with the president.
He said the economic policies of previous Congress governments had plunged the country into debt, and that the Hindu-nationalist coalition headed by the BJP had encouraged sectarianism.
"Under these circumstances, the Samajwadi Party will not support any party which is trying to form a government," Yadav said.
However, Amar Singh, the general-secretary of Yadav's party told reporters, "We don't want elections."
The Hindu-nationalist government led by Prime Minister Atal Bihari Vajpayee collapsed after Jayaram Jayalalitha withdrew the support of her regional party, known by its Tamil-language acronym, AIADMK. Jayalalitha met the president on Thursday and pledged the support of her 18 lawmakers to the Congress party.
The foreign origins of Gandhi, who was born in Italy, have been a point of contention for some of Congress' potential backers.
Gandhi, 51, the widow of Prime Minister Rajiv Gandhi, entered politics last year. She adopted Indian citizenship 16 years after her marriage.
Rajiv Gandhi, who was prime minister until 1989, was assassinated in 1991. His mother, Prime Minister Indira Gandhi, was assassinated in 1984.
By ASHOK SHARMA