Between last Thursday and Saturday, Paluckas secured 4,017 votes of the party's members, while Sinkevičius was supported by 3,654 members, the party told BNS.
Other candidates included MPs Andrius Palionis, Artūras Skardžius and former MP Mantas Varaška.
The second round of voting is scheduled for April 28-29, with the outcome to be announced on May 2 and the new leader to take the post during the Lithuanian Social Democratic Party's congress on May 6.
The Social Democrats, a member of the ruling coalition with the Lithuanian Farmers and Greens Union, is headed by ex-PM Algirdas Butkevičius who refused to seek reelection after the party's failed performance during the general elections of October 2016. The party secured 17 out of 141 mandates in Lithuania's parliament, finishing third.
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