The Karnataka leader's remarks came days after veteran Congress leader and former External Affairs Minister S M Krishna joined the BJP. Krishna, a former Karnataka Chief Minister, had also hailed the Prime Minister for his leadership.
Karnataka Assembly elections are due in the first half of 2018.
In a letter to Modi, Rajasekharan eulogised him for establishing a "direct rapport" with the electorate and for getting support from the poor and women cutting across religion and caste.
In 1971, Gandhi had given the call for removing poverty when the opposition parties called for 'Indira Hatao' (remove Indira).
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Rajashekaran in the letter said, "I would like to take this opportunity to convey my heartiest congratulations on the tremendous success of the BJP in the recent Assembly elections in the five northern states, specially on getting two-thirds majority in Uttar Pradesh and Uttarakhand."
Rajashekaran said Modi has been able to focus on poverty alleviation and empowerment of women to ensure their equal participation in all the development activities of the country.
"As you would kindly remember, Late Smt Indiraji, whileshe was the Prime Minister of this great country, for the first time gave the slogan 'Garibi Hatao' and got unbelievable support from the electorate.
The former Union Minister of State for Planning also wrote a letter to Union Minister M Venkaiah Naidu, congratulating him for the BJP's absolute majority in Uttar Pradesh and Uttarakhand.
"You have contributed so much to the success of the Indian democracy and its functioning," he wrote.