Sonia, the 67-year-old Congress party president, entrusted campaigning for the first time to her son and vice president Rahul, whose lacklustre performance failed to convince voters as Congress sought a third term in power.
"They both offered to resign but the party rejected it unanimously," member of parliament Amarinder Singh told reporters after a meeting of the party's top decision-making body in New Delhi.
Party spokesman Janardan Dwivedi said the Congress Working Committee had passed a unanimous resolution "to let Sonia Gandhi take whatever corrective steps are needed" to revitalise the party.
The Nehru-Gandhi dynasty has provided three prime ministers, including independent India's first, but analysts are increasingly questioning if it is the vote-winner it used to be.
"Economic growth and social mobility have radically transformed how younger Indians think and behave," leading historian Ramachandra Guha wrote in Kolkata-based The Telegraph newspaper at the weekend.
"No longer so deferential or unquestioning, they ask for evidence of Rahul Gandhi's own contributions apart from his family lineage. These are few," he concluded.
The Congress has ruled for all but 13 years of India's post-independence history and has run the country for the last 10 years at the head of the left-leaning coalition.
But the right-wing BJP's victory under hardline leader Narendra Modi has redrawn the political map.
Modi, 63, was set to call on India's President Pranab Mukherjee Tuesday to stake his party's claim to form the new government.
"It will be the first formal step before Modi is sworn in as prime minister," a source in BJP told AFP.
- Support for Rahul -
Speculation has swirled that Congress could call upon Rahul's younger sister Priyanka to play a greater role. She entered campaigning late in the election cycle to more favourable reviews than her brother.
About 50 Congress supporters chanted slogans for Rahul on Monday as party leaders, including outgoing prime minister Manmohan Singh, met for two-and-half hours.
"Rahul-ji, continue the struggle! We are with you!" the Congress supporters shouted.
"We want Rahul to take the forefront," Ahsan Raza, 30, a worker of the Youth Congress, told AFP outside the party headquarters.The party's defeat has been attributed to a sharp economic slowdown, rising food prices and a slew of corruption scandals, as well as Rahul being comprehensively overshadowed by Modi.
Dwivedi said Singh took responsibility on the "issues of inflation and corruption" at the meeting and said resignations by the Gandhis would serve no purpose.
"Manmohan Singh said that 'I take responsibility for the inadequacies of the government'. He told the party president (Sonia) and vice-president (Rahul) that their resignation was not the solution," Dwivedi said at a news conference after the meeting.
During his election campaign, Modi had slammed the dynastic culture of the Congress party while tapping into widespread anger over lack of jobs and development, offering a message of aspiration to the young electorate.
Dwivedi said Rahul accepted his part in the defeat and took blame for the debacle.
"Rahul said that the party lacks the kind of accountability that is needed, and that he could make a start by tendering his resignation.
"He said that probably he could not live up to the expectations that the party had from him."