ST. PETERSBURG, Russia » Not even a month ago, President Barack 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, Obama will arrive here for a meeting of the Group of 20 nations, and it is he as much as 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 Snowden’s disclosures about American eavesdropping on some of the very leaders who will be here with him, including Enrique Peqa 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 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 Assad, even if they share Obama’s concern about the use of chemical weapons.

Syria, even more than tensions between the United States and Russia generally, will overshadow the annual meeting of the G-20 leaders, which is normally devoted to the world’s economy. Under Russia’s leadership, this year’s agenda deals with economic stimulus, currency rates and efforts to discourage corporate tax evasion.

After reports of the chemical attack emerged on Aug. 21, Putin’s vehement opposition to any foreign intervention seemed at first to leave Russia embarrassingly isolated in its defense of Assad’s government. But in the weeks since, other nations and leaders have moved closer to his insistence that any intervention would be unlawful without the authorization of the United Nations.

"I want to draw your attention to one absolutely fundamental fact," Putin said in a lengthy interview with The Associated Press and the Russian state television network Channel One, published Wednesday. "In accordance with applicable international law, the authorization of the use of force against a sovereign state can only be given by the Security Council of the United Nations," he said. "Any other reasons, or methods, to justify the use of force against an independent and sovereign state are unacceptable and cannot be qualified as anything other than aggression."

In lieu of the meeting he was to have held with Putin in Moscow, Obama arrived in Sweden on Wednesday and defended his position on the imperative to respond to a gross violation of the international ban on chemical weapons, even as his senior advisers continued to make the case to a skeptical Congress at home.

"I didn’t set a red line," Obama said in Sweden, referring to his remark last year, later described as off-the-cuff, that the use of such weapons would cause him to rethink his evident reluctance to involve the United States deeply in the war in Syria, which has now claimed more than 100,000 lives. "The world set a red line."

Obama this week picked up support, albeit tepid in many cases, from the Republican congressional leadership for military action in Syria, and on Wednesday the Senate Foreign Relations Committee followed suit.

He can also claim credit for a steadily reviving U.S. economy, even as many formerly robust developing countries are experiencing weakness for the first time in years because of falling commodity prices and sagging currencies. Yet, even here, he faces challenges from countries that traditionally have been friends.

India, which also publicly opposed military action in Syria in a statement that refrained from assigning blame for the chemical attacks, has grown weary of U.S. economic policies as its own domestic woes have deepened, though Obama himself remains fairly popular.

India’s currency, the rupee, has lost 20 percent of its value since the spring, when Ben S. Bernanke, the Federal Reserve chairman, signaled an impending end to large-scale bond purchases, prompting foreign capital to flee emerging markets. "I think there is fatigue, quite frankly," said Siddharth Varadarajan, the editor of The Hindu, a leading newspaper. "Right now, the Indian economy is taking a beating because of what is happening in the U.S. Then there is a Syria crisis, which he has escalated, leading to higher oil prices."

Of Obama in particular, he added, "There’s not too much enthusiasm for his leadership."

The continuing leaks from Snowden, the former intelligence analyst who remains in hiding in Russia, have also roiled relations with allies in ways that could seed distrust of the Obama administration’s broader goals.

The debate over Syria erupted at an unusually low point in relations with Brazil, where the disclosure that the National Security Agency focused particular attention on the nation — and Rousseff personally — have soured the government’s view of the Obama administration.

Brazil’s foreign minister, Luiz Alberto Figueiredo, publicly rebuked the U.S. government this week, describing the spying as an unacceptable affront to Brazil’s sovereignty and demanding a written explanation of the American intelligence activities in the country.

Mexico’s foreign ministry addressed neither the debate over Syria nor the eavesdropping in a statement released as Peqa Nieto departed for St. Petersburg, but tensions in the relationship are palpable. Analysts in Mexico said the relationship was now spread across so many issues — trade, security, energy and migration, among others — and handled by so many overlapping agencies and institutions, that personal relations between presidents play far less of a role than it used to. That, in itself, suggested a recognition of Obama’s diminished stature.

Obama visited Mexico City in May, where he was said to have found some chemistry with Peqa Nieto, but they have both quickly been consumed by other issues. Indeed, a planned summit meeting of the United States, Mexico and Canada, which had been expected to take place this fall, has been pushed back to 2014.

"Everything was lined up during Obama’s visit to have an extraordinary advancement, and now that has been put into question because of the intensity of Barack Obama’s international and national problems, as well as Mexico’s problems," said Rafael Fernandez de Castro, an expert on U.S.-Mexico relations at the Autonomous Technological Institute of Mexico.

Obama is not the first president to face such skepticism. President George W. Bush faced vehement opposition — especially from France, Germany and Russia — over the war in Iraq, though he also had the strong support of allies like Britain. That opposition only grew in Bush’s second term, as it became clear that Iraq had no weapons of mass destruction and after the outbreak of sectarian killing that continues today.

Obama is now fighting that legacy as he makes the case for a more limited military response in Syria based on intelligence that he says is more concrete than that presented before the war in Iraq. Obama is also suffering from the heightened expectations that his presidency would bring a substantively new character to American leadership in the world.

Nina L. Khrushcheva, a professor of international affairs at the New School in New York, said that diplomacy under Obama, along with a general feeling of American overbearance, has left many more skeptical, and not just over crises like the wars in Afghanistan, Iraq, Libya and now Syria.

In St. Petersburg, a planned meeting with representatives of civil society groups was rescheduled so many times that several invitees from Moscow said Wednesday that they simply would not attend. "Honestly speaking, these meetings are rituals," said Lev A. Ponomaryov, a veteran rights advocate here. "It’s good we have them, but it is not the most serious issue during this trip."

Khrushcheva noted that many Chinese also felt slighted, for example, by the first lady’s failure to accompany Obama to his meeting with China’s leader, Xi Jinping, in California in June. "That ‘moral obligation’ in Syria, many feel is hard to argue with all the things the world has learned about the U.S. in the last 13 years," Khrushcheva said, "and sadly in Obama’s own five years."

© 2013 The New York Times Company