Ms Leuthard said Swiss troops were deployed on the demarcation zone between South Korea and North Korea and the country had a long history of neutral diplomacy.
"We are ready to offer our role... as a mediator," Ms Leuthard told a news conference.
"It is really time now to sit down at a table. Big powers have a responsibility."
South Korea said it was talking to the United States about deploying aircraft carriers and strategic bombers to the Korean peninsula after signs North Korea might launch more missiles in the wake of its sixth and largest nuclear test.
The UN Security Council has scheduled a second emergency meeting in a week about North Korea after a powerful nuclear test explosion added another layer of urgency for diplomats wrestling with what to do about the North's persistent weapons programmes.
Scheduled after North Korea said it detonated a hydrogen bomb underground on Sunday, the emergency session comes six days after the council strongly condemned Pyongyang's "outrageous" launch of a ballistic missile over Japan.
Less than a month ago, the council imposed its stiffest sanctions so far on the reclusive nation.
North Korea is "deliberately undermining regional peace and stability," the council said when it rebuked the latest missile test, reiterating demands for the country to halt its ballistic missile and nuclear weapons programmes.
North Korea said it tested an advanced hydrogen bomb for a long-range missile on Sunday, prompting a warning of a "massive" military response from the United States if it or its allies were threatened.
"We are not looking to the total annihilation of a country, namely North Korea," US Defense Secretary Jim Mattis said after meeting Donald Trump and his national security team.
"But as I said, we have many options to do so."
The US President previously vowed to stop North Korea developing nuclear weapons and said he would unleash "fire and fury" if it threatened US territory.
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