President Obama and German Chancellor Angela Merkel arrive for a group photograph at the Group of Seven summit on June 7 near Garmisch-Partenkirchen, Germany. (Carl Court/Getty Images)

Before he sat down with the leaders of the seven largest industrialized democracies here Sunday, President Obama met with German Chancellor Angela Merkel, a sign of how important their sometimes strained relationship has become to his presidency.

Obama toured a small Bavarian village with the German chancellor, and he kept the mood light. The president praised the alphorn music that greeted his arrival, drank a beer and joked about needing some lederhosen. Then the two leaders discussed for about 45 minutes some of the thorniest and most important foreign policy problems Obama is facing in the fourth quarter of his presidency.

The list Sunday included the financial crisis in Greece, sanctions designed to punish Russia for its aggression in Ukraine and two issues Obama views as critical to his legacy: progress against climate change and the passage of free-trade agreements in Asia and in Europe. Merkel’s support will be critical in all of those endeavors.

“Merkel is the European leader he openly admits he’s been probably the closest to, and yet that relationship has really weathered a number of storms over the last year,” said Julianne Smith, a former deputy national security adviser in the Obama administration and a senior fellow at the Center for a New American Security.

Germans were outraged in 2013 after information released by whistleblower Edward Snowden showed that the National Security Agency was monitoring U.S. allies’ communications, including those of Merkel. The scandal resurfaced last month when new revelations suggested that Berlin’s foreign intelligence agency, known as the BND, might have helped the United States gather intelligence on hundreds of European companies and politicians.

The result has been a “spike in anti-Americanism,” said Heather Conley, a senior vice president at the Center for Strategic and International Studies.

In her public remarks, Merkel referred generally to “differences of opinion” with the United States but said the two countries shared an essential partnership based on “mutual interests.”

White House press secretary Josh Earnest said the sensitive surveillance issues did not come up in Obama’s meeting with Merkel. Instead the two leaders, both pragmatists when it comes to foreign policy, focused on areas in which they could cooperate.

Obama needs Merkel’s help most acutely in Ukraine, where Russian separatists recently launched a new offensive. About half of his meeting with Merkel was focused on the way forward in what increasingly looks like a stalemated conflict, in which Russian President Vladi­mir Putin seems to believe that if he can hold out long enough, the resolve of Ukraine’s European allies will fracture.

Defense Secretary Ashton B. Carter, during a visit to Germany last week, conceded that tough economic sanctions had not curbed Putin’s aggressive behavior and suggested that other measures would be needed, though he did not specify what those might entail.

Obama has maintained that the only way to stop the fighting in Ukraine is through a diplomatic solution, driven by the sanctions regime that is in place. His message Sunday to the European allies, which would need to renew the sanctions at a meeting later this month, was to “stay vigilant” and focused.

That is where Merkel will be crucial. A fluent Russian-speaker, Merkel is the Western leader with the closest relationship with Putin.

“Obviously, Chancellor Merkel has played an important and leading role in preserving this unity,” Earnest said.

Less clear is what the White House and the allies will do if the increasingly fragile peace in Ukraine crumbles entirely.

Obama and the other Group of Seven leaders will need over the next few days to “try to forge a consensus” on how the West might respond if the Russians continue to escalate the fighting, said Charles Kupchan, White House senior director for European affairs. For now, the prospect of selling defensive weapons to Ukrainian forces, an idea that has little support among Washington’s European allies and relatively strong backing in Congress, appears to be dead.

The White House is also relying on Merkel to help forge a compromise with Greece that satisfies the country’s creditors without ruining its economy or forcing Greece out of the European Union. Such a collapse could cause volatility in global financial markets, hurting Europe and the United States.

On trade, Obama is pushing a 12-nation deal in the Asia-Pacific region, the Trans-Pacific Partnership, which faces staunch resistance from many in his party. If it succeeds, the president would like to conclude a similar deal with Europe, where Merkel’s assistance would again be essential to overcome resistance among some on the continent to free-trade deals.

The trade issue has become “something of a proxy for engagement in the world,” said Richard Fontaine, president of the Center for a New American Security.

Obama would like to emerge from the next two days of meetings with the G-7 allies with informal pledges to reduce greenhouse gas emissions ahead of a climate-change summit this year in Paris. It is an issue on which Obama’s goals and aspirations are largely in sync with those of Merkel and many of the other European leaders.

The meetings this week in Germany are an “important milestone on this issue,” said Ben Rhodes, a deputy national security adviser to Obama. “We can move both with announcing our own targets and taking steps to support other countries to protect the environment.”