In the annual televised speech, the Chancellor said: “The world is not waiting for us.”
Mrs Merkel said she is committed to quickly building a stable government for Germany in the new year.
The chancellor who failed to clinch a majority in September’s elections said in her speech that “some speak of a rift that goes through our society”.
She urged people to focus on the common ground and “respect” each other.
She said that “we become more aware of what holds us together, that we again emphasise common ground, that we endeavour to have more respect for others, these are my wishes for the new year.”
Germany has been without a proper government since the inconclusive elections in September.
Mrs Merkel called for Europe to work together and said nations must “represent their values”.
She said: “Germany and France want to work together to make that happen, and through that ensure Europe is ready for the future.”
Speaking about the rift in society, Mrs Merkel said: “Both are realities in our country: the success and the confidence, but also the fears and the doubts.
“Both of these are a motivation for me.”
Many people in Germany are angry that Mrs Merkel allowed more than a million migrants to enter the country in 2015-16.
In her speech, she spoke about people struggling to get a doctor’s appointment, and the people who worry about rising crime and violence and uncontrolled immigration.
Mrs Merkel and Emmanuel Macron promised to deliver a plan to reform the 19-nations euro currency.
The chancellor is hoping to form a coalition with the centre-left Social Democrats so she is able to form a government following the election in September.
One round of talks with the ecologist Greens and pro-business Free Democrats failed in November.