Ms Sonia Gandhi has confirmed she will not become India's next prime minister.
"I must humbly decline this post," she told a meeting of lawmakers from her Congress party.
Earlier, members of her Congress party and its political allies claimed Ms Gandhi was forwarding the names of Mr Manmohan Singh and Mr Pranab Kumar Mukerjee, both of whom were finance ministers, for the prime minister's post.
"There are rumours that her children are against her becoming prime minister, maybe because of security reasons," said Mr Somnath Chatterjee, an MP from the Communist Party of India-Marxist.
Ms Gandhi's husband, Rajiv, and her mother-in-law, Indira, were assassinated while prime ministers of the world's biggest democracy.
Earlier in the day, Ms Gandhi met President APJ Abdul Kalam but did not, as widely expected, leave with his approval to form a minority government that would be dependent on the outside support of two communist parties.
Ms Gandhi said she would meet with the head of state again tomorrow.