Kuncalienkar submitted his resignation to Assembly Speaker Pramod Sawant in the presence of BJP's Goa unit chief Vinay Tendulkar.
Tendulkar said the party has asked Kuncalienkar to vacate the seat to allow Parrikar to contest from there.
"It was the party's decision that Kuncalienkar should vacate his seat. The decision was convyed to him last night," he said.
"Parrikar had left it to the party to decide from where he should be contesting," he said.
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He has to get elected to the Assembly within six months for continuing as the chief minister.
The Panaji constituency has been Parrikar's bastion. He represented the seat from 1994 till 2014, before he moved to the Centre as defence minister in the Narendra Modi cabinet.
Kuncalienkar, who was then attached to the office of Parrikar, was given the ticket by the BJP to contest the by-election in the constituency, left vacant by Parrikar.
Kuncalienkar told reporters that his decision to resign was a "small sacrifice considering the big sacrifice made by Parrikar by resigning from the Union Cabinet to lead the government in the state".
"After the Assembly election results there was a unanimous decision that Manohar Parrikar should lead the government. The alliance partners too wanted the government to be led byParrikar," he said.
"Parrikar left the defence ministry in the Central Cabinet for the sake of Goa. The kind of sacrifice that Parrikar made is enormous. My sacrifice is very small as compared to his," he said.