As an international leader, Trump certainly does have a responsibility to all citizens of the world. Nationalities are simply titles, we are all part of a bigger human collective. And due to such a reality. we should have each other's best interests in mind. It is through this understanding that peace and harmony between countries can be established.
In other words, as the leader of one of the most powerful countries in the World, President Trump should promote and protect all human rights, not just human rights as they pertain to America, and not just when it is convenient. Trump should actively protect these rights throughout his presidency. What is the point of even proclaiming human rights if no world leader will follow them or call out their peers for failing to?