Chief Electoral Officer Praveen Gupta said all preparations for the counting of votes have been completed.
BJP state president Satish Poonia alleged that Congress misused government machinery to influence voters.
The Rajsamand assembly constituency was the centre of much controversy as some BJP-Congress workers had clashed on the eve of elections.
Sahara (Bhilwara) registered 23.94 percent, Rajsamand recorded 23.92 per cent and Sujangarh (Churu) recorded 21.9 per cent turnout, according to a spokesperson.
The duo, along with Rajasthan State Congress Chief, Govind Singh Dotasara, held public meetings in Sujangarh in Churu, Sahada in Bhilwara, and Rajsamand district to support the party candidates.
Poonia said that the BJP has already completed its groundwork in the constituencies before the announcement of the by-elections.
As the two leaders flew in the same helicopter, the effort was seen as a damage-control exercise to project a united face of the Congress party keeping in view the upcoming by-elections.
The seats of Mandawa in Jhunjhunu and Kheenvsar in Nagaur have been shared by the Congress and the RLP-BJP alliance.
Taunting his BJP party over its defeat in the Rajasthan bypolls, actor-turned-politician Shatrughan Sinha on Friday said the state had become the first to give the BJP "triple talaq".
The Congress Party today convincingly wrested Mandalgarh Assembly seat and achieved a huge victory in Ajmer and Alwar Lok Sabha seats in the Rajasthan by-polls.