WASHINGTON — For Barack Obama, a president who set out to restore good relations with the world in his first term, the world does not seem to be cooperating all that much with his bid to win a second.

That reality has been on vivid display in recent days. Europe has seemed unable to contain its rolling economic crisis to just Greece. The Syrian conflict has intensified as the United Nations suspended its observers’ mission amid the violence. Egypt’s popular revolution is at risk of being reversed by the military. And the Russians are cracking down at home and rattling sabers abroad.

As President Obama left on Sunday for an international summit meeting in Mexico, the daunting array of overseas issues underscored the challenges for an incumbent who is trying to manage global affairs while arguing a case for re-election. Although American voters are not particularly focused on foreign policy in a time of economic trouble, the rest of the world has a way of occupying a president’s time and intruding on his best-laid campaign plans.

If anything, the dire headlines from around the world only reinforce an uncomfortable reality for this president and any of his successors: even the world’s last superpower has only so much control over events beyond its borders, and its own course can be dramatically affected in some cases. Whether from ripples of the European fiscal crisis or flare-ups of violence in Baghdad, it is easy to be whipsawed by events.

The trick for any president, of course, is in not seeming to be whipsawed, even as his challenger presents him as weak and ineffectual in shaping international events. If a president cannot stand tall in the world, the argument goes, he is not up to the task of governing in a complicated age.

“Both candidates have to pretend that the U.S. presidency is far more influential over events than it really is,” said Stephen D. Biddle, a scholar at the Council on Foreign Relations. The obvious example is the European economic situation, which has profound implications for the American economy but is largely out of American hands.

“But to admit this is to look weak or to seem to evade responsibility,” Mr. Biddle said. “So both candidates tacitly agree to pretend that their policies are capable of righting the American economy while their opponent’s would sink it, when the reality is that both are in thrall to foreigners’ choices to a degree that neither would acknowledge.”

Mr. Obama’s trip to Mexico for a gathering of the Group of 20 leaders is his third international summit meeting in a month, reflecting the pull of priorities for any incumbent. While he confers in Los Cabos, his Republican challenger, Mitt Romney, will tour swing states. “I’ve still got my day job,” as Mr. Obama put it at a California fund- raiser last month.

The president will talk with European leaders about pulling out of the financial spiral after Sunday’s election in Greece, which gave the pro-bailout party a slim victory and the right to form a coalition government. He will also meet with President Vladimir V. Putin of Russia just days after the Obama administration accused Moscow of supplying arms to Syria in its bloody crackdown on the uprising there.

Just as Mr. Obama and Mr. Putin meet for the first time as presidents, their underlings will sit down in Moscow for the latest round of talks with Iran that are intended to curb Tehran’s nuclear program. The optimism over these talks this spring seems to have faded into fears of a further impasse that would play into Iran’s hands.

Little of this has played out on the campaign trail. In the latest New York Times-CBS News poll, only 4 percent of Americans picked foreign policy as their top election concern. Over all, polls show Mr. Obama with a double-digit advantage over Mr. Romney on foreign policy.

Yet Mr. Romney has occasionally turned to foreign policy to bolster his broader attempt to portray Mr. Obama as a failed president. On Saturday, he told a conservative coalition that when it came to Israel, he would “just look at the things the president has done and do the opposite.” On the CBS News program “Face the Nation” on Sunday, Mr. Romney said that on Iran “I would be willing to take military action, if necessary, to prevent them from becoming a nuclear threat to the world.”

Some Romney advisers said Mr. Obama was too willing to avoid accountability by presenting himself as a powerless bystander.

“These crises reflect an absence of leadership from the Obama administration,” said Kristen Silverberg, a former State Department official under President George W. Bush who is advising Mr. Romney. “He sat out the Iran protests, has faltered on Syria and let the Russians know he’ll be even more ‘flexible’ after our election. Global security and the strength of the global economy depend on strong U.S. leadership and a president who believes in America’s role in the world.”

Jamie M. Fly, executive director of the Foreign Policy Initiative, a conservative group, said there was a growing sense “that what is required is American leadership rather than the president’s leading- from-behind foreign policy that has failed to address an imploding Syria, a nuclearizing Iran, an economic crisis in Europe and a revanchist Russia.”

While foreign policy can pose its challenges, it has advantages for a president. Flying around the world on Air Force One to meet with the likes of Mr. Putin conveys a statesmanlike stature. It allows him to brush off criticism as just politics, as his campaign did with Mr. Romney’s comments about Israel over the weekend.

“Mitt Romney is yet again trying to score cheap political points by distorting President Obama’s record of support for Israel,” Ben LaBolt, an Obama campaign spokesman, said in a statement. “Our relationship with Israel is too important for Governor Romney to play politics with it.”

Mr. Obama assumes foreign policy will be an advantage for him, particularly because of his record of pulling troops out of Iraq, helping topple the government of Col. Muammar el-Qaddafi in Libya, taking robust action against terrorists and authorizing the raid that killed Osama bin Laden.

He is the “first real national security Democrat” since President John F. Kennedy, said James M. Goldgeier, dean of American University’s School of International Service. “He looks and acts like a commander in chief. So yes, the euro crisis, Syria, Iran, etc., can cause him problems. But Romney has his work cut out for him on foreign policy.”

Nancy E. Soderberg, a national security aide and United Nations diplomat under President Bill Clinton, says it is “par for the course” that an incumbent has to address international challenges while the challenger has a free ride.

But for all the attention on Syria, Egypt and other areas of conflict, the most important crisis for Mr. Obama remains the European economy because of its impact at home. “Europe’s weakness is likely to blow back on Obama’s efforts this fall — just at the wrong time,” she said. “He’ll have to run harder because of it.” (Copyright 2012 The New York Times Company 06/18/12)