As of 12 p.m., the over 50 per cent voter turnout was recorded in Colombo, Gampaha, Kalutara, Galle, Matara, Hambantota and Polonnaruwa, The Sunday Times said in a report.
Police Secretariat Chief DIG Sarath Peiris said that no incidents of violence have been reported so far.
Although, an unidentified group of gunmen first pelted stones and then open fire on two buses carrying voters in Mannar district.
No passenger was injured in the incident which is under probe.
Meanwhile, top political leaders and few of the presidential candidates also cast their ballots.
President Maithripala Sirisena voted in his hometown Polonnaruwa, Prime Minister Ranil Wickremesinghe exercised his franchise at the polling centre located within the Colombo University, while opposition leader Mahinda Rajapaksa cast his ballot in Medamulana.
Election front-runners, Sri Lanka Podujana Peramuna's (SLPP) Gotabhaya Rajapaksa voted in Nugegoda, while the New Democratic Front (NDF) alliance candidate Sajith Premadasa cast his ballot in Weerawila.
Long queues were seen 12,845 polling centres even before voting began at 7 a.m. Polling is due to end at 5 p.m., reports the Daily Mirror newspaper.
Nearly 16 million Sri Lankans were eligible to vote to elect their new leader from a crowded field of a record 35 candidates.
This is the highest number of contenders since the first presidential election in 1982. In 2015, only 18 had contested.
But Saturday's contest was mainly focused on the two front-runners.
Gotabaya (70) is retired soldier who took over Sri Lanka's defence portfolio during the period when his older brother, Mahinda Rajapaksa was President (2005-2015) and also when Sri Lanka ended its war in 2009 with the Liberation Tigers of Tamil Eelam (LTTE).
While the family's political future appeared to be fading after Mahinda's defeat in 2015, the April 21 Easter bombings that killed 269 people, lent wings to Gotabaya's candidacy.
While campaigning, he presented himself as a nationalist and champion of the Sinhalese Buddhist majority, while also promising strong national security in the wake of the April attacks.
On the other hand, Sajith Premadasa, the son of Ranasinghe Premadasa who served as the President from 1989 until he was assassinated in May 1993 by the LTTE, has pledged to fight for the Muslim and Tamil minorities.
The votes from the minority community had also played a major role in Sirisena's 2015 victory.
Anura Kumara Dissanayake, the leader of the Marxist party, Janatha Vimukthi Peramuna (JVP) which led to youth insurrections in 1971 and 1987-1988, has emerged as the third popular candidate, followed by former Army Commander Lt. Gen. Mahesh Senanayake who formed National People's Party (NPP) after he left the army last August.
If Premadasa wins the election, the incumbent cabinet and government would continue until the next general election to elect lawmakers. But if Gotabaya Rajapaksa is elected and proves 113 majority power in Parliament, there is a possibility of a change of government.
Election Commission officials have said that the results were expected by Saturday night.
( With inputs from IANS )