"They break, we unite. They ignite fire, we douse it. They get angry, we love. This is the difference between them and us," he told party workers.
Gandhi, who was heralded by the 132-year-old party's top brass, family members and boisterous rank-and-file, alleged that Prime Minister Narendra Modi was taking India back to the medieval times.
In his first speech to party workers after his formal takeover, he set the tone of its future course and how the party would take on its arch-rival BJP, saying the Congress was for inclusive politics and that it respects all Indians that extends even to the ruling party.
"Today, the BJP people are trying to spread fire and violence in the entire country and only the force of lovable Congress workers and leaders can stop them," he said.
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Before he gave his first address, he sought his mother Sonia Gandhi's blessings and kissed her on the forehead.
Attacking Modi, he said the Congress took India into the 21st century, "while the prime minister today is taking us backward, to a medieval past where people are butchered because of who they are, beaten for what they believe and killed for what they eat".
In an emotionally charged final speech as the Congress chief while passing on the party's mantle to her son, Sonia Gandhi said the grand old party should set its house in order and introspect while readying for any sacrifice to stop communal forces in the country.
She exuded confidence that Rahul would lead the party with courage, patience and devotion. He has endured many personal attacks which have made him "fearless", she said.
"We are all witness to daily attacks on our fundamental values, against the freedom of speech and expression, against our rich diverse culture, and an atmosphere of fear and suspicion is being created.
"Amid this, the Congress must look within and introspect and forge ahead. If we do not stand by our principles, we will not be able to wage this fight for the common people. This is a moral battle and to achieve success, we must set our house in order and be ready for any kind of sacrifice," she said.
She recalled the times when she entered politics after losing her "anchor" (Rajiv Gandhi) and "mother" (Indira Gandhi), and how with the support of Congress workers she steered the party to power both at the Centre and in state after state.
Congratulating Rahul Gandhi on his elevation, she said personal attacks on him have made him fearless and voiced confidence that his leadership will infuse new vigour in the party.
"I am confident that with a new and young leadership, our party will be reinvigorated and bring about changes we need. You have chosen Rahul as your leader. He is my son, and it is not right for me to praise him," she said.
In his brief address at an event where the new Congress president was handed over a formal certificate by the party's election authority, Singh said certain "disturbing trends" are noticeable in the country's polity and the people were depending on Rahul Gandhi to transform it.
Singh described the day as "unique" in the party's history and said Rahul Gandhi's leadership would bring a new sense of dedication and commitment to steer the party to greater heights of glory.
"As a distinguished academic pointed out a few days ago, there are dangers that the politics of fear will take over from the politics of hope," the former prime minister said, apparently targeting the BJP.
"May your path be blessed," he said as he ended his speech.
Rahul Gandhi was given the certificate in the presence of Sonia Gandhi, Priyanka Gandhi Vadra and Robert Vadra and several senior party leaders.
The new party chief also met PCC delegates from various states thanking them for electing him unopposed.
While there was bursting of crackers outside the venue, women played with 'gulal' and young party workers danced to the beats of 'dhol'.
Posters and banners were put up in Lutyens' Delhi and traffic was halted around the AICC office on Akbar Road.