In a letter to her son Sandeep Dikshit, Manmohan Singh said that he learnt "with profound sorrow" about the "sad and shocking news of the untimely demise of our beloved Sheila Dikshitji".
He said the people of Delhi had a deep affection for her and "that is why she holds the distinction of being the only woman Chief Minister in the country who has led her party to three consecutive victories in Assembly elections".
"In her death, our country has lost a great administrator and an outstanding leader who contributed enormously to all-around development of Delhi," he said.
Gandhi said he "shared a close personal bond" with her.
"I'm devastated to hear about the passing away of Sheila Dikshitji, a beloved daughter of the Congress Party, with whom I shared a close personal bond. My condolences to her family and the citizens of Delhi, whom she served selflessly as a three term Chief Minister, in this time of great grief," he said in a tweet.
Senior party leader Mallikarjun Kharge also condoled her death, terming it a huge loss for the Congress and Delhi.
"This is a huge loss to both the Congress and Delhi. The Congress workers will remember her as someone who alwas stepped up and fought for the party whenever the situation demanded," he said in a letter to her son.
Kharge also said that Delhi's people will always remember her as a popular leader and distinguished Chief Minister who led them for 15 years and transformed New Delhi into a world class capital city".
Congress General Secretary K.C. Venugopal said that in Dikshit's death, the "country has lost a bold political personality and a strong party leader who dedicated her life until her last breath to the party and the common man".
Party spokesperson Randeep Singh Surjewala, in a tweet, said: "The ever smiling humanist, the conscientious administrator, the infrastructure building politician, the dedicated soldier of party, the woman who reshaped Delhi..... We'll always miss you, and so will Delhi.... Deepest Homage!"
Dikshit passed on Saturday afternoon at a private hospital following a cardiac arrest. She was 81.
( With inputs from IANS )