SEOUL, South Korea — North Korea said Wednesday that its nuclear weapon program was no longer negotiable and indicated that it might conduct its third nuclear test to retaliate against the United Nations Security Council’s tightening of sanctions against the isolated yet highly militarized country.

Although it was not the first time North Korea issued such strident rhetoric, its posture, coming under the new leadership of Kim Jong Un, threw a direct challenge to President Obama as he starts his second term, and Park Geun-hye, who will be sworn in as South Korea president next month.