Turnout was at nearly 70 percent an hour before polling stations closed at 4:00 pm (1030 GMT), an election commission official said, citing provisional figures.
Premadasa's appeal came hours after the government told an all-party meeting in New Delhi that India is naturally worried over the Sri Lankan crisis and ahead of the presidential election in Sri Lanka on Wednesday to pick a successor to ousted president Gotabaya Rajapaksa.
Minutes before nominations formally opened Premadasa tweeted that "for the greater good of my country that I love and the people I cherish" his party will support Dullas Alahapperuma, a former media minister, to replace Gotabaya Rajapaksa who resigned last week.
Sajith Premadasa, chief of the Samagi Jana Balawegaya party, made the threat in parliament.
Premadasa, 52, also stepped down as the Deputy Leader of the United National Party (UNP) with immediate effect.
The election will see a close contest between former wartime defence secretary Gotabaya Rajapaksa, 70, and the ruling party candidate Sajith Premadasa, 52. Anura Kumara Dissanayake from the National People's Power (NPP) coalition is also a strong candidate.