Trailng Cozart in the top-five were Chris Owings from the D-backs (219,287) and the Nationals' Trea Turner (180,184).
The next ballot update will be on June 5.
Fans may cast votes for starters at MLB.com and all 30 club sites -- on computers, tablets and smartphones -- exclusively online using the 2017 Esurance MLB All-Star Game Ballot until Thursday, June 29, at 11:59 p.m. ET. On smartphones and tablets, fans can also access the ballot via the MLB.com At Bat and MLB.com Ballpark mobile apps. Vote up to five times in any 24-hour period for a maximum of 35 ballots cast.