She was 81.
Kakodkar, the daughter of former Goa chief minister Dayanand Bandodkar, died around 1.10 PM, her son Samir Kakodkar told PTI.
The Goa government has announced two days state mourning, while all government offices were given holiday today.
Family sources said that she was ailing for six months and was bed-ridden since the last one month.
Following her father's death in 1973 while being still in office, she became chief minister and continued to be in power till being ousted by the split within Maharashtrawadi Gomantak Party in 1979.
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Goa Chief Minister Laxmikant Parsekar expressed condolences over the death of Kakodkar.
"We have lost the woman whose contribution in the development of the state was immense," he said.
The Chief Minister said though Kakodkar was not active in politics, he always approached her for guidance.
"We are orphaned by the death of Kakodkar. She has been a crusader of regional languages," Subhash Velingkar, convener of BBSM, said.
MGP President Deepak Dhavalikar said in her death Goa has lost an "Iron lady".
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