Before the closed-door meeting that lasted around 40 minutes, Merkel congratulated Erdogan over his June 24 presidential election victory.
Erdogan was accompanied by National Defense Minister Hulusi Akar, Foreign Minister Mevlut Cavusoglu and Presidential Spokesman Ibrahim Kalin.
The two-day NATO summit started with the attendance of 29 NATO heads of state and government to make important decisions on the future of the alliance.
The summit is shaping up to be one of the most difficult alliance gatherings in years as Trump continues to pressure NATO allies to increase their military spending.
NATO headquarters says the alliance is on track to increase its overall defense spending by 3.8 percent in 2018, and a total of eight members are expected to reach the 2 percent benchmark by the end of 2018.
Jens Stoltenberg, NATO's secretary general, for his part, credited Trump at their July 11 breakfast meeting for pushing NATO countries to increase defense spending -- noting that European countries and Canada are expected to "add an extra $266 billion to defense between now and 2024."