BERLIN — Angela Merkel of Germany, addressing her country as an acting chancellor, pledged in her annual New Year’s address on Sunday to work for all Germans and to swiftly form a new government to help ensure success into 2018 and beyond.

In a sobering assessment of the divisions in German society that led to a fragmented result in the Sept. 24 election, Ms. Merkel acknowledged that despite the country’s economic strength, many Germans feel left behind. She promised to “have an eye on the needs of all citizens” in order to “meet the challenges of the future.”

The new year will bring the weakened Ms. Merkel her own challenges, as she struggles to form a new government with her old partners after failing to assemble a different coalition.

Exploratory talks with the Social Democrats will begin on Jan. 7, amid intense pressure to avoid another election. Many fear it would strengthen Alternative for Germany, the nationalist, populist party that won its first seats in Parliament in 2017.