SEOUL, South Korea — North Korea has sent a letter to the office of President Park Geun-hye of South Korea, threatening “retaliatory strikes without warning” if anti-Pyongyang rallies by conservative activists in Seoul are not stopped, officials here said on Friday.

North Korea has often used such heated language against the South and the United States. But its latest threat came amid concerns that the North Korean leader, Kim Jong-un, might stage an armed provocation to raise tensions with the outside world and encourage domestic unity after the Dec. 12 execution of Jang Song-thaek, his uncle and presumed mentor.

For analysts and policy makers in the region, Mr. Jang’s execution after being convicted of treason raised disturbing questions: Was it a sign of instability within the secretive government, and if so, will North Korea’s hard-line military provoke the South in an attempt to raise its profile?

On Thursday, Defense Secretary Chuck Hagel said at a Pentagon news conference that the execution of Mr. Jang highlighted the unpredictability of the Pyongyang government, and that the “reality of that uncertainty heightens the tensions.”