The country's powerful National Defense Commission said it would never deal with South Korean President Lee Myung-bak, a conservative who stopped a no-strings-attached aid policy toward the North in 2008.
North Korea also said in its stern message that they are uniting around Kim Jong Un, referring to the late leader's son for the first time with the title, Great Leader. That title was previously used for his father.
It was the latest incremental step in a burgeoning personality cult around the son following the Dec. 17 death of Kim Jong Il.
The younger Kim on Thursday was pronounced Supreme Leader of the ruling party, military and people at a massive public gathering on the final day of official mourning for his father.
The country's top levels of government appear to have rallied around Kim Jong Un in the wake of his father's death.
However, because he is only in his late 20s, there are lingering questions outside North Korea about his leadership of a nation engaged in delicate negotiations over its nuclear program and grappling with decades of economic hardship and chronic food shortages.
Experts say the North's statement is a warning for Seoul not to take the new leadership lightly.
The Associated Press contributed to this report.