Yes and no. Every new president sets a mandate for NASA. The past few administrations have been setting mandates for Mars missions, the current administration wants to go to the Moon.
The big difference between all these and the Apollo project is NASA's budget. The Apollo mandate included a huge increase in NASA's budget, to 4% of the total federal budget. These days, NASA's budget is only 0.5% of the total federal budget and new mandates are not accompanied by a budget increase. So any large-scale mandate such as Mars or Moon missions ends up being unattainable before the next election (and the next potential change in mandate).
The most recent mandate is by president Trump:
President Trump has formally told NASA to send U.S. astronauts back to the moon. "The directive I'm signing today will refocus America's space program on human exploration and discovery," he said.
NASA has huge ongoing commitments (programs like the ISS) that it can't cancel at a whim to free up money for a Moon or Mars mission.
NASA has done lots of work that will inform a Mars mission if it ever gets off the ground. For example, the ISS has been very valuable in teaching us how we can live in space for longer periods, which is research we'll need for e.g. a Mars mission.