Parrikar is pitted against Congress' Girish Chodankar and Goa Suraksha Manch's (GSM's) Anand Shirodkar.
"I want a good victory margin. I am requesting voters to come out. My concern was whether they will come out in large numbers or not because of the Ganesh Festival being closer on August 25," Parrikar told reporters on the last day of the campaigning.
The chief minister said he became confident of a good turnout after he met voters.
Parrikar, currently not a member of the state Assembly, had represented Panaji constituency during 1994 to 2012.
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He had resigned as MLA in the year 2014, following his ascension to Centre as Defence Minister.
"I have met several people and now I am positive that people will come out in large numbers," Parrikar said.
The BJP stalwart said he had chaired as many as 120 informal meetings in the Panaji constituency in the run-up to the by-election.
"After staying away from Panaji for almost three years during my stint as Defence Minister, I got an opportunity to meet people and know their issues. I have understood all their problems which would be solved soon after the elections are over," he said.
The election was necessitated after the BJP's sitting MLA Siddharth Kuncolienkar vacated the seat for Parrikar, as he has to get elected to the Assembly within six months of becoming the Chief Minister.
Bypoll will also be held for Valpoi assembly seat on Wednesday, where Congress rebel Vishwajit Rane is contesting on the BJP ticket against Roy Naik, the son of former state home minister Ravi Naik, of Congress.