ST. PETERSBURG, Russia — Not even a month ago, President Obama canceled a planned summit meeting with President Vladimir V. Putin, citing Russia’s decision to grant asylum to Edward J. Snowden as evidence of a broader deterioration of relations. “We weren’t going to have a summit for the sake of appearances,” the president’s deputy national security adviser, Benjamin J. Rhodes, said then.

On Thursday Mr. Obama will arrive here for a meeting of the Group of 20 nations, and it is he as much as Mr. Putin who has to worry about appearances.

He heads into the gathering facing questions about his leadership and his policies at home and abroad — from his threat to respond to the use of chemical weapons in Syria to efforts to revive the flagging global economy to Mr. Snowden’s disclosures about American eavesdropping on some of the very leaders who will be here with him, including Enrique Peña Nieto of Mexico and Dilma Rousseff of Brazil.

Given diplomatic niceties, any public confrontation at the newly refurbished Constantine Palace on the Gulf of Finland near here is unlikely, but Mr. Obama’s standing on the world stage has undoubtedly suffered from the recent turmoil. That has complicated his relations not only with Russia and China, but also with allies like Germany and Britain, which have refused to endorse military action against the forces of Syria’s president, Bashar al-Assad, even if they share Mr. Obama’s concern about the use of chemical weapons.