She offered to resign from her post in response to a political revolt by three senior party leaders, but the offer of resignation was immediately rejected by members of the powerful Congress Working Committee, which formulates party policy.
In the capital, Delhi, nearly 2,000 of Mrs Gandhi's supporters shouted angry slogans against the rebels, calling them "traitors". In Bombay, her supporters and opponents clashed outside the party's office.
Because of her non-Indian ancestry, some in the party have questioned the Italian-born Mrs Gandhi's claim to become India's next prime minister.
The dissidents - Sharad Pawar, Purno Sangma and Tariq Anwar - are also members of the Working Committee. The trio wrote a stinging letter at the weekend to Mrs Gandhi, proposing an amendment the constitution to bar foreign-born citizens from becoming prime minister.
Mrs Gandhi joined politics last year, following in the footsteps of her late husband, the former prime minister Rajiv Gandhi, seven years after he was assassinated. She has been projected as the prime ministerial candidate by her party for the September-October federal elections.
Hours before the party leadership was to hold a meeting to discuss the letter, Mrs Gandhi's supporters burnt an effigy of Mr Pawar in Bombay, provoking scuffles between rival groups. Posters were torn down at the party's Bombay office and a sign board ripped off.
Meanwhile, Mrs Gandhi rallied supporters to fend off the challenge. Demonstrators in trucks and buses converged near her home and at party headquarters shouting "Long live Sonia Gandhi".
Discussions reportedly were under way about the possible expulsion of the three rebels from the party.
Their letter read: "It is not possible that a country of 980 million people, with a wealth of education, competence and ability, can have anyone other than an Indian, born of Indian soil, to head its government."
It also said the party's top candidate should have a "track record in public life". Mrs Gandhi has never held elected office. (AP)Reuse content