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Hajduk have won their domestic league six times, although for the last three years they have had to settle for the runners-up spot behind Dinamo Zagreb.
Fulham's potential opponents RNK finished just behind their city rivals last season to cap a meteoric rise after three successive promotions and are playing in Europe for the first time.
Diego Godin, among those introduced at half-time, headed a corner over in the 83rd minute as Atletico were held.
In his team's first pre-season game, Simeone opted for a strong XI as the likes of Griezmann, Yannick Carrasco and Jan Oblak started.
Leo Baptistao shot over the angle under pressure from Lukasz Piszczek after 11 minutes before Pierre-Emerick Aubameyang fired wide from 10 yards when he should have scored.
At full-stretch, Mario Gotze could only touch a lofted throughball straight at goalkeeper Pau Lopez and, with Dortmund dominating possession, Gonzalo Castro drove a shot just over the crossbar after a powerful run.
Diego Simeone's men struggled to create much of note in the scoreless draw against the Liga MX side at the Estadio Nemesio Diez.
Star forward Antoine Griezmann played the first half, but the La Liga giants lacked creativity, perhaps understandable as they continue preparations for the season proper.