The euro zone is imploding. The Japanese have moved to hold down their currency, leaving little room to criticize China for doing the same.

Efforts to write consistent rules for global finance or coordinate policy on any grand scale remain a tangle. The U.S.’s struggle with its own economy and public debt has hobbled its authority.

As the Group of 20 convenes its annual summit on Thursday, the rhetoric will — as usual — focus on the benefits of cooperation and the strides nations are making to further it. But in terms of concrete action, this might be the meeting where an organization meant to nudge the global economy in a more efficient direction recognizes its limits.

At the height of the financial crisis in 2009, the group agreed on the need for a massive government stimulus plan that for a brief moment had China, Europe, the U.S. and others pulling in the same direction. But those entities have been pulling on different oars ever since.

The stimulus agreement “provided a very strong sense that indeed it was the committee that ran the world. ... After that, every single G-20 meeting has been less impactful than the prior one,” said Moises Naim, a senior associate at the Carnegie Endowment for International Peace.

The G-20 includes the top industrialized nations as well as the major emerging economic powers such as China and Brazil. Major international organizations such as the International Monetary Fund also participate in the talks.

With an already sluggish global economy showing signs of slowing further, officials said they hope their two-day summit will produce substantive action to bolster world growth.

But the meeting here on the French Riviera has been noticeably overshadowed by events in Greece and elsewhere, and by a sense that the world’s great powers aren’t immune to the whims of small nations.

Greece’s surprise call for a referendum that might prompt its exit from the euro zone has dominated discussion and forced the summit host, French President Nicolas Sarkozy, to call emergency talks over a crisis in his own back yard.

He had hoped to use his year-long chairmanship of the G-20 to push on broad and long-term global economic reforms — changing the international monetary system and finding ways to ease the effect of commodity prices swings on poor countries.

Instead he is battling to keep the euro intact.

“We won’t let the euro be destroyed. We won’t let Europe be destroyed,” Sarkozy said after the emergency talks Wednesday ended in an ultimatum that Greece either comply with the economic rigors needed to stay in the euro zone or prepare to withdraw from it.

A follow-up meeting among the G-20’s euro zone members — France, Germany and Italy — was called for Thursday morning. European stocks, buoyed briefly by crisis plans announced in Brussels last week, continued a recent slide when markets opened this morning.

“The most important aspect of our task over the next two days is to resolve the financial crisis here in Europe,” President Obama, who arrived early Thursday and immediately met with Sarkozy, told reporters. He said he agreed with the French president that “the E.U. has made some important steps towards a comprehensive solution. ... We also discussed the situation in Greece and how we can work to resolve that situation as well.”

It was hardly an auspicious start to the summit. And problems with other nations are also brewing.

A decision in Switzerland to hold down the value of its highly prized currency and the general instability in the euro region have combined to push world investors toward the Japanese yen. That poses a burden for Japan, effectively making its all-important exports more expensive as it tries to rebound from this year’s devastating earthquake.

The result: On the eve of the summit, the Bank of Japan moved heavily into currency markets to push down the price of the yen.

Though rationalized as a response to the country’s post-earthquake woes, the currency move was an example from one of the world’s major economic powers of the type of uncoordinated policy move the G-20 is supposed to moderate.

It also leaves little room for the group to make any statement about China’s management of its exchange rate. The United States has tried to use the G-20 as a neutral forum to push the Chinese on its currency and other policies regarded as critical to making that export powerhouse begin buying more from other nations. The effort has produced little in the way of concrete results and has, if anything, become more complicated.

The United States had hoped the G-20 could be a forum where major nations would compare detailed notes about their economies and agree to target specific goals.

But “they are oblivious to metrics and scrutiny when drafting their communiques and their decisions,” Naim said. “It is quite amazing to see the pledges and the promises ... that have not materialized, pledges and promises of changed behavior that we have not seen, promises of reforms that have gone only halfway.”

U.S. and other officials say that the organization continues to prove its worth. In September, G-20 leaders leaned hard on the 17 euro zone countries to do more to contain their problems, and extracted a promise that they would agree to a new program by the time of the Cannes meeting.

They did. Then the rest of the world intervened.