Leuthard said Swiss troops were deployed on the demarcation zone between South Korea and North Korea and noted that her country - along with Sweden - had a long history of neutral and discreet diplomacy.
But China and the United States had to take their share of responsibility, she added, warning of "over-reactions".
Sanctions "did not change many things" in terms of convincing Pyongyang to abandon its weapons programmes even though North Korea's population had suffered, Leuthard said.
A day after the North's largest nuclear test yet, Seoul said on Monday it was talking to Washington about deploying aircraft carriers and strategic bombers to the Korean peninsula after signs Pyongyang might launch more missiles.
"I think it really is time for dialogue," Leuthard told a news conference in Berne.
"...We are ready to offer our role for good services as a mediator. I think in the upcoming weeks a lot will depend on how the U.S. and China can have an influence in this crisis. That's why I think Switzerland and Sweden can have a role behind the curtain."
"I think that's our role to look at what kind of possibilities we find. Because, well, Twitter won't be an adequate instrument... This must be very discreet."
Noting that the Communist Party congress in North Korea's neighbour and ally China was due to take place in October, Leuthard said the time for such initiatives was not ideal, so "perhaps this was also part of the plan of North Korea."
North Korean leader Kim Jong-un spent part of his youth in Berne studying under an assumed name.
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