South Korea's president has expressed concern and frustration with North Korea's continuing threats.

In a speech Friday to graduating military cadets, President Park Geun-hye said she will "deal strongly with North Korea's provocations." She called the current security situation "very grave."

Earlier Friday, North Korea announced it will void non-aggression pacts with South Korea as of Monday . The North also said a telephone hotline with Seoul, in existence for more than four decades, will be severed.

Pyongyang's threats came after the U.N. Security Council voted unanimously Thursday to approve new sanctions against the North, in response to its latest nuclear test. A sanctions resolution received important backing from North Korea's historical ally, China.

North Korea has been issuing threats at South Korea and the United States, whose armed forces are conducting joint military maneuvers on South Korean soil.

On Thursday, North Korea's Foreign Ministry threatened a pre-emptive nuclear strike on the U.S. The ministry framed the threat as its "right to pre-emptive nuclear attack against the headquarters of the aggressor." It also said the United States is about to "ignite a nuclear war."

North Korea also has threatened to void the 1953 armistice that ended the Korean War, and it announced a series of military exercises to compete with drills being held by the U.S. and South Korean forces. Pyongyang has threatened five times since 1994 to scrap the armistice, but in each instance has stopped short of doing so.

North Korea's rhetoric has become more heated following international condemnation of its February nuclear test and December missile launch.