In the address, Kim Jong-un highlighted last year's developments in inter-Korean and US-North Korea relations, while calling on his country to seek economic development and modernize its defense industry.
Kim met US President Donald Trump to discuss denuclearisation in June 2018 but with few results so far.
North Korea, however, would have "no choice but to defend our country's sovereignty and supreme interest, and find a new way to settle peace on our peninsula", if the United States "misinterprets our people's patience, and makes one-sided demands and continues down the path of sanctions and pressure on our republic".
The New Year speech is a key fixture in the North Korean political calander, setting the agenda for the year to come.
But for most of his 30-minute speech, he focused on North Korea's economy and said he stands ready to resume projects with South Korea and restart operations at a jointly run factory park in the border town of Kaesong.
Kim has warned Washington not to test North Koreans' patience with sanctions and pressure.
In the joint declaration, Kim pledged to work towards the complete denuclearization of the Korean Peninsula, while in return, Trump promised to provide certain security guarantees to North Korea. "The challenge, however, is will Team Trump be willing to back away from its position of zero sanctions relief?" said Harry Kazianis at the Washington-based Centre for the National Interest.
Last year's rapprochement came after a turbulent 2017 marked by North Korea testing missiles that could reach the United States mainland and an escalation in rhetoric between Pyongyang and Washington with both sides trading insults and threats of nuclear destruction.
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He was referring to his landmark summit with US President Donald Trump in Singapore in June, when he said he had "fruitful talks" and "exchanged constructive ideas".
On the front page of the ruling party's flagship newspaper was Kim touring monuments to capitalism, stepping out of a Chinese jet and smiling while shaking hands with the "imperialist" USA president.
Wearing a black suit and a grey-blue tie, Mr Kim said: "Now that North and South Korea chose to take the path of peace and prosperity, we insist that joint military exercises with outside forces should no longer be allowed and deployment of war equipment such as outside strategic assets should be completely stopped".
Trump has been considering a second summit with Kim to speed up the stalling denuclearization.
The North Korean leader "obviously had certain expectations that the United States would take certain steps - however rudimentary they are - after the North blew up a nuclear test site and took other steps".
Mr Kim congratulated himself on his diplomatic activities during 2018, including meetings with South Korean president Moon Jae-in and Chinese president Xi Jinping. The North used a blunt statement last month to reiterate its traditional stance on denuclearization, saying it will never unilaterally give up its weapons unless Washington removes what Pyongyang describes as a nuclear threat.
Seoul and Washington are in a security alliance and the United States stations 28,500 troops in the South to protect it against its neighbour, which invaded in 1950.
Although Pyongyang did not conduct nuclear or missile tests past year, satellite images have pointed to continued activity at the North's related facilities.