SEOUL, South Korea — President Park Geun-hye ordered the South Korean military and police on Monday to increase vigilance, especially along the disputed western sea border with North Korea. She warned that the North might attempt armed provocations after the recent purge and execution of Jang Song-thaek, who was believed to have been the North’s second most powerful official.

“Given the recent series of incidents in North Korea, there is uncertainty over the direction in which the political situation there will develop,” Ms. Park’s office quoted her as saying during a meeting with senior aides. “We cannot rule out contingencies like reckless provocations from the North.”

Ms. Park’s warning about what she called “the gravity and unpredictability of the current situation” came as officials and analysts in the region were scrambling to determine what Mr. Jang’s execution might mean for the stability, internal politics and foreign policy of North Korea, an opaque, nuclear-armed nation with an inexperienced leader, Kim Jong-un, who is believed to be 30 years old.

Mr. Jang, who was Mr. Kim’s uncle and had been regarded as a mentor, was executed on Thursday after being accused of plotting to overthrow the government. His downfall was startling not only because of who he was, but also because of the unusually public way in which he was purged.