"I have deeply appreciated our many meetings and conversations about all the issues involved in developing the German-American and the transatlantic relationship, not least in overcoming the global financial and economic crisis," she wrote in a letter released by her office.

Merkel said she and Obama had "worked together closely these last years in a spirit of friendship" and said she hoped to welcome him back to Germany soon.

She also cited their cooperation on Afghanistan, where Germany has the third largest military contingent after the United States and Britain, and efforts to convince Iran to abandon sensitive nuclear work.

"I look forward to continuing all this cooperation so both our countries can continue to stand side-by-side to contend with the important foreign policy and economic challenges that we face as friends and allies," she wrote.

"I wish you continued strength and success in the second term before you."

Merkel, a conservative who faces an election next year, has placed a priority on transatlantic ties during her two terms but frequently clashed with Obama and his team on the right response to the European debt crisis.

While Merkel has argued that debt reduction is crucial to make economic growth sustainable, Obama has said that excessive austerity could snuff out any recovery and threaten the global economy.