WASHINGTON — In the nearly two weeks since Egypt’s military seized power, President Obama has promoted a better federal bureaucracy, given a medal to George Lucas of “Star Wars” fame and had former President George Bush to the White House for lunch. What he has not done is publicly address the violent upheaval in Cairo.

That is not to say Mr. Obama is uninvolved. In the privacy of the West Wing, away from the cameras, he has made calls to leading figures in the Arab world and has met with advisers trying to influence the crisis. But his low public profile on issues like immigration, Syria and health care underscores a calculated presidential approach that admirers consider nuanced and detractors call passive.

While other presidents have put the bully in the bully pulpit, Mr. Obama uses his megaphone, and the power that comes with it, sparingly, speaking out when he decides his voice can shape the trajectory of an issue and staying silent when he thinks it might be counterproductive. In his first year, the president seemed to be everywhere, talking about everything. In his fifth year, he is choosing his opportunities — even if it appears he is not always in command of events.

Some compare Mr. Obama’s approach to the “hidden hand” style of President Dwight D. Eisenhower, who often steered events behind the scenes without being public about his role. Jim Newton, the author of “Eisenhower: The White House Years,” a book with back-cover blurbs from Defense Secretary Chuck Hagel and Secretary of State John Kerry, said Mr. Obama was like the former president in avoiding major international conflict, relying more on covert action and letting Congress take the lead in legislation.