Parrikar, the former Defence Minister, won by 4803 votes, defeating his rival from Congress Girish Chodankar.
The prime minister also congratulated BJP's Vishwajit Rane on his electoral victory in Valpoi constituency.
"Congrats to @manoharparrikar & @visrane for the impressive wins in Panaji & Valpoi respectively. I thank the people of Goa for their support," Modi tweeted.
Rane retained his Valpoi seat by defeating his nearest rival Roy Naik of the Congress by 10,066 votes. Rane had resigned as MLA after leaving the Congress.
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