The stabilization of Afghanistan, the global financial crisis, climate change and Iran's controversial nuclear program require closer cooperation, the spokesman said in a statement following Thursday evening's telephone call.
Merkel also congratulated Obama on his "historic" election victory, the statement said.
The president-elect thanked Germany for the warm welcome he received in Berlin when he addressed a crowd of around 200,000 in July. Obama had also met with Merkel during his Berlin visit.
Obama telephoned various foreign leaders after his Nov. 4 election victory.
Merkel and Obama are expected to meet when the chancellor travels to Washington on Nov. 14 for the world financial summit.
Once in office, Obama is expected to press Germany to increase its involvement in Afghanistan by sending troops to the volatile south of the country.