The state-run Korea Central News Agency reported that Kim pledged to "work hard to bring earlier the new era in which the ideals and desires of our people will come true."
His letter also purportedly thanked the people for trusting his party in tough times.
"I offer thanks to the people for having invariably trusted and supported our party even in the difficult times," Kim said.
"I sincerely wish all the families across the country greater happiness and beloved people, good health."
He was expected to skip his usual televised address on Jan. 1.
Typically under economic duress, the Hermit Kingdom appears to face especially rough conditions in the new year.
In addition to facing U.S. sanctions, the nation also encountered a pandemic-related border closure with its main source of commerce -- China.
KCNA added that North Koreans had completed an "80-day battle" in reference to a push to increase productivity before major political events. "[T]he all-people advance by dint of self-reliance," it reported, brought "a proud victory of the historic 80-day battle."
Kim is expected to speak this month to address his ruling party - the first time he will have done so in five years.
The Associated Press contributed to this report.