Mr Jaitley, who has campaigned in the state in the run-up to the elections, told reporters, "The BJP estimates that we will not only get a comfortable but a landslide win. In most places people of all sections have supported the BJP".
The early reports, the minister said, has been encouraging for the BJP. "We are grateful to the voters that they came out in large numbers to vote... The BJP has got great support in this phase," he said.
Saurashtra and Kutch that have the maximum number of constituencies that voted today, are crucial. The party that wins the most seats in these regions will be seen to have a head start.
The sprawling Saurashtra region, which covers 11 districts, is home to a huge section of Patidars, traditional BJP voters who are now at odds with the government for its lack of support to their demand for quota in jobs and education. The face of the Patidar agitation, 24-year-old Hardik Patel, who is too young to contest an election has vowed to bring down the BJP government and is supporting the Congress.
Surat, the state's diamond and textile hub, is a BJP stronghold. But this year's election there is seen to be a referendum on the government's move last year to ban high denomination notes of Rs 500 and Rs 1000, and the rollout of the flagship Goods and Services tax.
Claiming that the small traders of the area bore the brunt of both measures, Congress's soon-to-be-chief Rahul Gandhi has urged the voters to punish the BJP. Mr Jaitley and Smriti Irani have defended the GST and demonetisation, trying to allay the concerns of the traders.
The next phase of elections is on Thursday when the rest of the state votes. The counting of votes will take place on December 18.