Aggressive statements from North Korea were given in response to the United States issuing statements or sanctions against them, or supportive measures that favor South Korea. Threats against the United States also have political value in North Korea.
One of the most significant threats the North Korean government has made to the U.S. in recent years was on March 29, 2013, when they said that missiles could reach the U.S. mainland and that the governmental focus had "naturally entered the state of war," according to The Independent reporting on their state news agency, KCNA. This was prompted by two United States stealth bombers flying over North Korea, the purpose of which was to remind them the U.S. was prepared to defend South Korea if they attacked. Other exchanges like this have occurred for events like North Korean missile tests, such as that in 2009 and 2013, and increasing international scrutiny towards North Korea, such as with June 2015's U.N. Human Rights report.
North Korean state media is highly negative towards South Korea and the United States, and most problems that afflict an average North Korean, such as food shortages, power outages and water problems, are blamed on their interference. Engaging in public and negative rhetoric towards these entities is a reliable way for the North Korean government to keep their populace supportive of the government and unwilling to cooperate with South Korea.