In their summit communique, G8 leaders also committed themselves to promoting growth alongside fiscal responsibility.
However, the leaders acknowledged “the right measures are not the same for each of us”.
Greece’s possible exit from the eurozone was high on the agenda, following inconclusive elections there.
The leaders of France, Germany, the US, the UK, Italy, Japan, Canada and Russia have been meeting at Camp David in the US state of Maryland.
“We agree on the importance of a strong and cohesive eurozone for global stability and recovery, and we affirm our interest in Greece remaining in the eurozone while respecting its commitments,” the statement said.
The global economic recovery was showing signs of progress, they said, but “significant headwinds persist”.
G8 leaders are divided on whether to continue with austerity or back stimulus measures instead.
German Chancellor Angela Merkel favors austerity, while newly elected French President Francois Hollande wants to pursue policies for greater growth, as does President Barack Obama.
There are caveats but the first line of the communique – about promoting growth and jobs – means Presidents Obama and Hollande have won the day.
However, it is not clear that Angela Merkel has got their message and is prepared to act on it, our correspondent adds.
US officials said Angela Merkel would hold a one-on-one meeting with Barack Obama later on Saturday.
Italian Prime Minister Mario Monti said there would be another key meeting in June in Rome, where he would host Francois Hollande and Angela Merkel.
Earlier, UK Prime Minister David Cameron called for deficit reduction.
“There is a growing sense of urgency that action needs to be taken, contingency plans need to be put in place and the strengthening of banks, governments, firewalls and all of those things need to take place very fast,” he told reporters at Camp David.
The likelihood of Greece leaving the euro is growing.
The office of the Greek interim prime minister said on Friday that Angela Merkel had suggested the country hold a referendum on euro membership on election day, but the German chancellor’s cabinet dismissed this as “false”.
Greek voters will again go to the polls on 17 June after earlier elections failed to produce a viable coalition to run the country.
A caretaker government was sworn in this week after elections.
Investors fear any refusal by Athens to impose deep spending cuts agreed under a bailout deal could result in the country quitting the bloc of 17 countries that use the euro.
Two opinion polls published on Saturday showed the anti-bailout left-wing Syriza bloc neck and neck with centre-right New Democracy, both on about 25%.
Larger countries such as Spain or Italy struggling to ease their debt loads might then become vulnerable, potentially triggering wider eurozone upheaval and even a global financial crisis to rival the one of 2008.
The G8 summit has now moved on to other issues, including food security, energy and climate, partnerships in North Africa and the Middle East and the war in Afghanistan.
After the G8 summit ends on Saturday evening, most of the leaders will decamp to Chicago to join a larger group of international officials for a NATO summit on Sunday and Monday, at which Afghanistan is expected to be the main item on the agenda.
Three men arrested in Chicago on suspicion of planning to throw petrol bombs at the NATO summit have been charged with conspiracy to commit terrorism and possession of an explosive or incendiary device.
Prosecutor Anita Alvarez said the campaign headquarters of President Barack Obama and the home of mayor Rahm Emanuel were among the targets.
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