Switzerland has plenty of strengths to draw on in an uncertain world climate, she said, citing the strong economy, low unemployment and the capacity to innovate, however its success lies in cohesion and solidarity.
"We want to preserve our stability and continue on this path to success. For that we must stick together more than ever. Our society is strong because it knows how to reconcile different interests," she said, stressing the importance of uniting people across the cultural, linguistic and country-city divide.
The Federal Council will try to seek compromise, she added.
“That implies that we will listen to each other and try to understand one another. It's not easy.
"In an era dominated by new technology, exercising democracy is more difficult than ever," she added.
“I want to thank everyone who, day after day, contributes to the cohesion of our society, to mutual understanding, progress and openness,” she concluded.
Her words comes after a difficult year in which the Swiss government sought a way forward following a 2014 referendum on immigration, which divided the country and threatened its relationship wth the EU.
Parliament's solution, achieved in December, was seen as a necessary compromise by some, and undemocratic by others.
Leuthard takes over the Swiss presidency for 2017 having previously been president once before, in 2010.
Also the minister for the environment, transport, energy and communication, she is the longest-serving member of the seven person Federal Council and served as vice-president last year.