SEOUL, South Korea — For years, North and South Korea have hurled invective at each other that would do Shakespearean characters proud.

The North’s insults usually follow an anti-imperialist line — “American puppets” is a favorite — though “traitors” and “running dogs” are also usual fare. And then there was the personal insult last year against Park Geun-hye, the South’s first female president, with a reference to the “venomous swish” of her skirt.

The South’s oratory is usually less strident, but conservative activists have been known to pick up the slack, railing in public against the man many in North Korea see as a godlike figure, calling the young leader, Kim Jong-un, a diabolical tyrant, “a little pig” and “an immoral brat.” Then they burned him in effigy.

Now, North Korea has made what it called an “important proposal,” suggesting on Thursday an end to the mudslinging as a way to smooth over relations that reached a low last year. The North also said it would begin unspecified steps to help ease military tensions along the disputed western sea border.