The Congress was leading in eight seats in Goa and the ruling BJP in five of the 40 constituencies in the state after the first three hours of counting of votes.
Chief Minister Laxmikant Parsekar is trailing Congress's Dayanand Sopte in Mandrem constituency.
The first result went in favour of the Maharashtravadi Gomantak Party (MGP), whose contestant Dipak Pawaskar defeated Ganesh Gaonkar of the BJP in Sanvordem.
Leader of Opposition Pratapsinh Rane (Congress) is ahead of BJP's Vishwajit Krishnarao Rane in Poriem seat.
Other Congress contestants who established early leads include Jeniffer Monserratte in Taleigao, Chandrakant Kavlekar in Quepem and Francis Silveira in St Andre seat.
While Goa Forward Party has gained lead in two seats, NCP leads in one.
The MGP is ahead in Bicholim seat as well, with its candidate Naresh Sawal mantaining lead over BJP's Rajesh Patnekar.
Pravin Zantye of the BJP is leading in Mayem against Congress candidate Santosh Sawant.
The state had witnessed a keen tussle between the Congress and the BJP, while the AAP has also put up a spirited fight in 39 seats.
The MGP, which broke alliance with the BJP before elections, had formed a three-party front with the Shiv Sena and Rebel RSS leader Subhash Velingkar-led Goa Suraksha Manch (GSM).