Election office sources said nearly 20 per cent of the electorate cast their ballots by mid-day and the exercise was going on peacefully.
The bypolls were necessitated after Uttar Pradesh Chief Minister Yogi Adityanath and Deputy Chief Minister Keshav Prasad Maurya vacated the Gorakhpur and Phulpur Lok Sabha seats, respectively following their election to the state legislative council.
After casting his vote in Gorakhpur, Adityanath said the BJP was getting widespread support from the people.
Attacking the BSP and the SP, the chief minister said, "These parties are indulging in negative politics, politics of bargaining and politics of opportunism. The state has suffered the negative consequences (of SP and BSP).
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"And in order to ensure that in future such situations do not arise, efforts have to be made to shun politics of casteism and dynastic politics, and focus on development and administration," he said.
When asked to comment on the SP and BSP entering an electoral understanding, he said, "This will have no effect. I had wanted that in this bye-election if the SP, BSP and Congress had fought together, then results would have been much better (for us)."
The saffron party has fielded Kaushalendra Singh Patel from Phulpur and Upendra Dutt Shukla from Gorakhpur against the SP's Pravin Nishad and Nagendra Pratap Singh Patel, respectively. The Congress has nominated Sureetha Kareem for Gorakhpur and Manish Mishra for Phulpur Lok Sabha seat.
Ten candidates are in the fray from Gorakhpur, while 22 candidates are contesting from Phulpur.
Gorakhpur is significant for the BJP as it is the bastion of the chief minister, who represented the seat in the Lok Sabha five times. Prior to Yogi Adityanath, the seat was represented in parliament by his mentor Yogi Avaidyanath thrice.
Exuding confidence that the BJP would sweep the ongoing Lok Sabha bypolls in the state, Maurya today said the 2014 Lok Sabha record would be repeated by the saffron party.
"I am confident that on March 14, the record which was made in Phulpur in 2014 (Lok Sabha general elections) will be repeated, and our candidate Kaushalendra Patel will emerge victorious," he told reporters after casting his vote for Phulpur parliamentary constituency along with his family members.
"But, today from the UP's point of view, poll alliance of the BJP, Apna Dal (Sonelal) and Suheldev Bhartiya Samaj Party (SBSP) exists. Apart from this, we do not have any other alliance. And, banking on this alliance, we will win 80 out of 80 Lok Sabha seats in the state," he said.
Taking a jibe at the SP-BSP tie-up, the minister said, "Their (SP-BSP) votes will be transferred only when they have enough votes. The votes (of the people) are with us. But, they have only leaders who make statements...The voters of Mayawatiji have deserted the BSP and have reposed their faith in Modiji, Yogi and BJP. We are winning both the Lok Sabha seats, and with wider margin".
In Gorakhpur parliamentary constituency, there are 970 polling centres and 2,141 polling booths, while in Phulpur, there are 793 polling centres and 2,059 polling booths.
According to the Election Commission, there are 19.61 lakh voters in the Phulpur parliamentary constituency, while the Gorakhpur Lok Sabha seat has 19.49 lakh electorates.
As many as 4,728 Voter Verifiable Paper Audit Trail (VVPAT) machines are being used in the bypoll and provisions for web-casting from 95 critical booths have been made.