He said that his party would make history as the only party to come into power within a short span of time since its formation, defeating other old political parties.
"We are confident of the SLPP recording a historic victory. We hope for a two-thirds majority at the election but it is up to the people to decide," he said.
He said he is confident that the economy can be revived under the leadership of President Gotabaya and Prime Minister Mahinda.
The results would be announced by Thursday evening, Deshapriya said.
President Gotabaya voted in his Colombo suburb polling station while his elder brother and the prime ministerial aspirant Mahinda voted in his home constituency in the southern district of Hambantota.
"We are hopeful of winning two-thirds support," Mahinda, 74, told reporters after voting.
He said his younger brother Gotabaya's election as president was endorsed by 6.9 million voters last December and that he was hopeful of securing the same support.
Former prime minister Ranil Wickremesinghe said that only his party, the United National Party, was capable of turning around the economy which is currently in poor state due to COVID-19 and mishandling by the current government.
Mahinda's SLPP is expected to win control of the 225-member assembly by a comfortable margin, according to analysts.
President Gotabaya hopes for a two-thirds majority for the SLPP so that he can amend the Constitution to restore presidential powers curbed by a 2015 constitutional change.
The president is not a candidate while Mahinda is running from the north western capital district of Kurunegala.
Poll stations were manned by over 8,000 health officials who supervised the maintenance of health guidelines to prevent the spread of COVID-19.
The election, which was postponed twice due to the coronavirus, is to elect a 225-member Parliament for a 5-year term.
Over 16 million people were eligible to vote to elect 196 out of a total of 225 lawmakers for the next five years. Twenty-nine others will be named from a national list according to the number of votes received by each party.
The election, originally scheduled for April 25, was put off until June 20 as the COVID-19 outbreak hampered the preparations.
The August 5 date was later fixed as the health authorities issued guidelines for holding the poll.
Some 20 political parties and 34 independent groups are in the fray with over 7,200 candidates from 22 electoral districts.
Former president Maithripala Sirisena is running from the north central region of Polonnaruwa under the SLPP banner while former prime minister Wickremesinghe and former leader of the Opposition Sajith Premadasa are running from the Colombo district.
(Only the headline and picture of this report may have been reworked by the Business Standard staff; the rest of the content is auto-generated from a syndicated feed.)
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