Top world leaders gathering in Camp David on Friday will confront renewed financial tensions in Europe and a deepening quandary over how to bolster tepid economic growth in developed nations while controlling public debt.

It will be the first summit of leaders from major industrialized countries since the euro region completed a set of extraordinary measures meant to combat its problems. The discussions will focus on an urgent question: Will those steps protect Europe and the world economy if the crisis worsens, or can more be done?

The immediate threat comes from political turmoil in Greece and the increased prospect that it will leave the euro zone rather than carry out a tough austerity program rejected by Greek voters in elections last week. The fear is that a Greek exit could undermine the confidence of global investors in other struggling European countries such as Spain and Italy, raising the prospect that these major economies could default if they do not get an international bailout.

The impact of Greece leaving the euro zone could be grave not just for Europe but also for the United States, prompting a downturn in trade that would hurt U.S. companies and roiling global stock and credit markets.

The world economy is already in fragile state, with the U.S. recovery still anemic, many European countries in or near recession and growth slowing in other major economies such as China.

Heading into the Group of Eight summit, hosted by President Obama, officials from outside the euro area are worried whether emergency measures taken over the past years by European leaders — including hefty bailout funds and inexpensive loans to struggling banks — are adequate. A recent surge in the cost that Spain and Italy have to pay to borrow money shows that investors are worried also.

“They’ve got a long way to go, a very difficult set of challenges, and they just need to make sure that they can convince the world that they’re going to manage these challenges,” U.S. Treasury Secretary Timothy F. Geithner said at a forum in Washington on Tuesday. “We have a big stake in the managing.”

In Britain and Canada, G-8 members whose governments have been among the euro zone’s harshest critics, the alarm bells were ringing.

British Prime Minister David Cameron said in Parliament on Wednesday that the euro region was “looking at potential breakup” because of Greece’s political paralysis and differences among countries over the best economic policy. “That’s the choice they have to make, and it is a choice they cannot long put off,” he said.

Britain’s central bank chief spoke of a “storm” heading toward the country, which is not part of the euro currency union.

The leaders from Germany, France and Italy — the three euro-zone countries in the G-8 — will be in the hot seat at the summit, at the Camp David presidential retreat in western Maryland. That is a position those countries’ leaders have often been in since Greece’s problems began unfolding in late 2009.

Two of the leaders are relative newcomers with much left to prove. Italian Prime Minister Mario Monti took office in November and, while given credit for taking a tougher line on government spending, has yet to win parliamentary approval for broader labor and regulatory policy changes considered central to boosting growth. Newly elected French President Francois Hollande wants more emphasis on economic growth but could face skepticism at the meeting if he proposes to do that by increasing government debt.

In Greece, a caretaker government was appointed Wednesday to stay in office until a fresh vote in June, now seen as a national referendum on whether to stay with the euro and accept the terms of an international bailout worth hundreds of billions of dollars.

European leaders have begun discussing whether to relax the bailout terms. German Chancellor Angela Merkel in Berlin on Wednesday said she may be open to some centralized European investment in Greece to help lift its economy from a five-year recession.

Even broader questions will be on the table at Camp David, including how the developed world can bolster growth when governments are constrained by high debt and have little room for stimulus spending.

With unemployment at record levels in the developed world, the question of how to balance growth and austerity has become central in the G-8, a group composed largely of the world’s industrialized “mature” economies. The group still accounts for the bulk of world economic output, but its members are struggling to remain competitive with fast-growing Asian and Latin American nations.

More immediately, G-8 leaders will debate whether the programs put in place over the past year can absorb the shock of a Greek exit.

Euro-area leaders have pledged a trillion dollars of their taxpayers’ money to a regional bailout fund, largely paid for by Germany and France. The European Central Bank has loaned more than a trillion dollars since December to European banks to ensure they have the cash to keep operating through the crisis. And most members of the larger European Union have agreed to closer central review of annual budgets.

But interest rates on Spanish bonds — which have risen to dangerous levels — is one piece of evidence that Europe’s crisis-fighting effort has not worked as intended. The very creation of a large bailout fund — a financial “firewall” — was supposed to help Italy and Spain by proving that euro-zone countries would stand behind each other with emergency help as needed and convince investors that there was no further risk of the kind of massive losses suffered by owners of Greek bonds.

In Madrid on Wednesday, Prime Minister Mariano Rajoy said the threat to Spain remained, and officials in the country fear a Greek exit from the euro would prompt investors to flee their country — despite Europe’s pledges to stand behind it.

“Right now there is a serious risk that [investors] will not lend us money or they will do so at an astronomical rate,” Rajoy said, according to news reports from Madrid.

Ahead of the G-8 gathering, Canadian Finance Minister James Flaherty said he worried it may be impossible for leaders of euro-zone countries to follow through on the steps needed to address their problems.

“The whole future of the euro zone is up for grabs,” Flaherty said.

Staff writer David Nakamura contributed to this report.