She has also written separately to former prime ministers Sher Bahadur Deuba and Madhav K Nepal.
In her letter to Koirala, who is also the president of Nepali Congress, she said that the Indian National Congress wholeheartedly supports the rescue and relief operations being undertaken by the Indian Air Force and Army and spoke about the "historic relationship" between the two countries.
"There exists a natural affinity between the people of India and Nepal," she said.
"The tragic loss of thousands of lives and the enormity of destruction have saddened us all. I myself and on behalf of the members of the Indian National Congress convey our heartfelt condolences to the people of Nepal.
"...I take this opportunity to assure you of our continued solidarity with your government and support to the people of Nepal in this moment of crisis," she said.
In her letter to Deuba and Nepal, she reiterated the same.