BERLIN — German Chancellor Angela Merkel secured a decisive victory in federal elections Sunday, winning enough votes to form a new ruling coalition that should give her a freer hand to govern and provide support for closer ties with Washington.

Enhancing her reputation as the continent’s top political power broker, Merkel became the first leader of a major European country to win re-election since the global financial crisis struck last year.

Voters generally approved of her response to the recession, even though it has hammered Germany’s export-dependent economy and has resulted in a huge amount of public debt.

German voters ignored warnings in recent days from leaders of the Taliban and al-Qaida that they would punish Merkel’s government for sending troops to Afghanistan — German forces represent the third-largest foreign contingent there, behind the U.S. and Britain.

Although surveys show that a majority of Germans oppose the war, analysts said Merkel is unlikely to join other European countries, such as Italy, that have called for a quick withdrawal of forces.

“We don’t want to forget that there are many problems in our country to be solved,” Merkel told a cheering crowd in Berlin. “I think that tonight we can really celebrate, but I would say that after that there is work waiting for us.”

Merkel, 55, grew up in the former East Germany. She enjoyed a warm personal rapport with President George W. Bush but got off to a cool start with the Obama administration.

She and her ministers were quick to blame the global recession on Wall Street and Washington, even though German banks had gobbled up huge amounts of toxic assets, and German exporters had profited handsomely from the free-spending ways of U.S. consumers.

Analysts said her government has sought to repair some of the damage by toning down criticism and collaborating more closely on issues such as the oversight of international financial markets.

They noted that Obama and Merkel appear to have improved their comfort level with each other and worked productively together at last week’s Group of 20 summit in Pittsburgh.