In his first major statement since his United National Party (UNP) foiled ex-president Mahinda Rajapaksa's comeback bid, Wickremesinghe struck a note of reconciliation.
"I want everyone to come together now. Think of the country, think of the people," he told a spray of television cameras on the lawn of his official residence.
"We can achieve unity, progress in this country if we work together."
Wickremesinghe, 66, who has led a minority government since President Maithripala Sirisena beat Rajapaksa in a presidential election in January, said he expected to be sworn in as prime minister.
Although his centre-right party fell tantalisingly short of a parliamentary majority, it can count on supporters of Sirisena from the opposition Sri Lankan Freedom Party (SLFP) to control parliament and push ahead with reforms.
Wickremesinghe said he would soon meet Sirisena to discuss the next government's makeup and policy agenda that will be presented to parliament when it convenes on Sept. 1.
In one key decision, Finance Minister Ravi Karunanayake told Reuters he expected to be reappointed to the post.
Sirisena had clashed with Rajapaksa, who ran for prime minister on an SLFP ticket, and a political realignment could leave the former president isolated in a rump opposition, as he and his allies face a series of corruption investigations.
Rajapaksa, whose alliance polled just three percent behind the UNP and who won the district he ran in with more than 400,000 votes, is still revered by many for ending a 26-year Tamil insurgency in 2009.
Asked whether his call for unity included Rajapaksa, Wickremesinghe said: "It includes everyone."
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