"19.59 per cent polling was reported till 11 a.m. The polling has been going on peacefully," a senior Election Commission official said.
Vice President Hamid Ansari, Congress chief Sonia Gandhi, party Vice President Rahul Gandhi, AAP leader Arvind Kejriwal, BJP's chief ministerial candidate Kiran Walia and Union Minister Harsh Vardhan were among the early voters.
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The Delhi polls are seen as a direct contest between AAP and BJP and have been billed as a referendum on Prime Minister Narendra Modi, a description rejected by his party leaders.
This is the second assembly polls in Delhi within little over one year. The assembly polls in December 2013 had resulted in a hung verdict with BJP emerging as the single largest party with 31 seats and AAP making a stunning debut by wresting 28 seats while the ruling Congress got only 8 in the 70-member assembly.
The elections are significant as a defeat for BJP may bolster the opposition while a victory for the party will increase its confidence ahead of assembly polls in Bihar later this year.
Kejriwal, who led AAP's spirited campaign, today expressed confidence the party would get a clear mandate, saying truth would triumph in the polls.
"I am confident that AAP will win the elections and form government in Delhi," he sa after casting his vote at B K Dutt colony in his New Delhi constituency.
His BJP rival Kiran Bedi, after casting her vote at a polling station in Malviya Nagar, appealed to people to come out in large numbers and vote.
"Today is a historic day. Delhiites have to decide what kind of Delhi they want - a clean Delhi, a secure Delhi, a capable Delhi, a Delhi that respects women. Respecting women is respecting Delhi. I appeal people to come out and vote," she said.