Still, for a naturally reserved president who has assiduously cultivated a handful of leaders, it has been a dispiriting stretch.

Prime Minister Recep Tayyip Erdogan of Turkey, whom Mr. Obama views as a new kind of Muslim leader, has used tear gas and water cannons against protesters in Istanbul. Mohamed Morsi, the Muslim Brotherhood leader whom Mr. Obama telephoned repeatedly after he became president of Egypt, later granted himself unlimited powers, though he also cut off ties with Syria.

Mr. Obama spent nearly four years befriending Mr. Putin’s predecessor, Dmitri A. Medvedev, hoping to build him up as a counterweight to Mr. Putin. That never happened, and Mr. Obama now finds himself back at square one with a Russian leader who appears less likely than ever to find common ground with the United States on issues like Syria.

Administration officials argue that their bet on Mr. Medvedev made sense at the time and yielded benefits, not just in an arms treaty but also in Russian support for sanctions against Iran, acquiescence to the NATO operation in Libya and agreement to allow American troops to travel through Russian airspace to Afghanistan.