Obama chose Camp David in part to encourage a freewheeling discussion out of sight of most media and potential protests, allowing the leaders to sit around a cabin table to negotiate terms, or stroll through the leafy paths for chats that seemed a world away from the typical summit convention-hall setting.

It all came before Obama was to lead a much larger NATO summit in Chicago on Sunday and Monday that will be heavily focused on the Afghanistan war.

The drag of a eurozone crisis comes as joblessness and doubts about a life of better opportunities are already the chief concerns for American voters.

In their united view, the leaders conceded some points about Merkel’s push for austerity, saying budget deficits must close.

But their joint statement added that budget cutting should ‘‘take into account countries’ evolving economic conditions and underpin confidence and economic recovery.’’ That suggested a willingness to let indebted countries take more time to reduce their deficits in line with eurozone rules in order to lessen the deadening impact of cuts on the economy.

It also called for ‘‘investments in education and in modern infrastructure,’’ which would involve more government spending. That approach also meshes exactly with Obama’s campaign-year strategy for accelerated economic growth, which is to keep spending money on core priorities while taking on the debt through cuts and higher taxes.

The statement of support for Greece remaining in the euro underlines the unpredictable damage to the global financial system that could come from a Greece departure. It follows a week of increasing speculation that Greece might not be able to stay the course, and in which a top European Union official said officials were working on emergency plans in case of a Greek exit. That country is facing the most acute financial crisis of the eurozone and is set to hold elections June 17 to end political deadlock.

At issue is whether Greece abandons the euro to escape austerity measures. Meanwhile, Europe’s woes have given shudders to Wall Street.

The Fitch ratings agency dropped Greece to the lowest possible grade for a country not in default Thursday. Fitch said Greece’s departure from the euro ‘‘would be probable’’ if elections next month do not reverse political trends there, which have brought in politicians opposed to the terms of Europe’s bailout.

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