Parrikar, who is Rajya Sabha MP from Uttar Pradesh, voted at around 11 am at the Goa Secretariat at Porvorim. The former defence minister is yet to be elected to the Legislative Assembly since he took charge of the state in March this year.
Goa Forward Party's (GFP's) Jayesh Salgaoncar and Vinod Palyekar, Congress' Philip Neri Rodrigues, Ravi Naik, Digambar Kamat and Tony Fernandes, and BJP's Pramod Sawant and Pravin Zantye were among the early voters.
The current strength of the 40-member House is reduced to 38 in the wake of the resignations of Vishwajit Rane (Congress) and Siddharth Kuncolienkar (BJP).
Three MPs from the state - Shantaram Naik (Rajya Sabha), Shripad Naik (Lok Sabha) and Narendra Sawaikar (Lok Sabha) will cast their votes in Delhi.
GFP, a BJP ally, is supporting the NDA candidate Ram Nath Kovind.
GFP leader and state minister Vinod Palyekar said his party had taken the right decision to support Kovind. "We are part of the NDA. There is no question of voting for anyone else," he said.
Salgaoncar, who is the incumbent Housing Minister, said the GFP is supporting Kovind as "he is a good leader".
All three MLAs of another BJP ally, the Maharashtravadi Gomantak Party (MGP) also cast their vote.
The MGP had extended support to Kovind.
"We have voted for the UPA candidate Meira Kumar. Everyone voted as per conscience," he said.