Patients with Parkinson's disease (PD) have difficulties performing a dual task (DT) while walking and may use the "posture second" strategy. It is not clear if this is a result of motor or cognitive impairments. We examined the effects of explicit prioritization of walking or the cognitive task on gait speed (GS) and variability in 20 patients (Hoehn & Yahr stage: 2.3 ± 0.5) and 20 healthy older adults during usual-walking and under three DT (verbal-fluency) conditions: (1) no instruction for prioritization, (2) specific attention to the walking pattern (gait prioritization), and (3) specific attention to the cognitive task (prioritization of verbal-fluency). The Montreal Cognitive Assessment, the Frontal Assessment Battery, and the Trail Making Tests assessed cognitive status. The two groups did not differ on these cognitive tests. Compared to usual-walking, all subjects reduced their GS in the un-instructed DT condition. Compared to the un-instructed DT condition, both groups significantly (p < 0.001) increased GS when prioritizing walking and maintained about the same GS when prioritizing the cognitive task (p > 0.155). All three DT conditions increased gait variability in both groups (p < 0.001 usual-walking compared to uninstructed DT). Verbal-fluency tended (p = 0.073) to be influenced by prioritization in both groups. Task prioritization abilities were similar in the patients and controls, even though the patients generally walked more slowly. PD patients without cognitive impairment apparently utilize their cognitive resources in the same manner as healthy older adults. Both groups, however, use some form of the posture second strategy and naturally focus on the cognitive task.