North Korean leader Kim Jong-un says he is "open to dialogue" with South Korea in the New Year, but has warned the US he has a "nuclear button" on his desk to use if threatened.

Tensions escalated on the Korean Peninsula throughout 2017 over a series of missile tests conducted by the North, and Pyongyang's pursuit of a nuclear weapons programme.

In a televised New Year's speech on Monday, Kim said improving ties between the North and South is an "urgent issue".

"It's a grave matter to which the entire Korean nation needs to put its efforts towards resolving," he said.

"Contacts and dialogues between the North and the South will expand exchanges and cooperation and we should dispel mutual misunderstanding and distrust, and take responsibility in our role as the main agent for reunification."

South Korea's presidential office welcomed Kim's speech, which included a proposal to send North Korean athletes to Winter Olympics in Pyeongchang next month, the country's state news agency, Yonhap, reported.

"We welcome that Kim expressed willingness to send a delegation and proposed talks as he acknowledged the need for improvement in inter-Korean ties," presidential spokesperson Park Soo-hyun said on Monday.

Possible motives

Al Jazeera's Florence Looi, reporting from Seoul, said South Korea is willing to hold talks "any time, in any form" with Pyongyang.

"But we have to ask ourselves what is Kim Jong-un hoping to gain from this and some analysts have said that he is perhaps hoping to drive a wedge between the US and South Korea because these two are traditional allies," she said.

"It is also possible that North Korea is trying to buy more time as it tries to improve its nuclear capabilities."

North Korea will continue to focus on "mass producing nuclear warheads and ballistic missiles for operational deployment" in 2018, Kim said in his address.

He repeated previous claims that the entire US is now within range of North Korea's nuclear arsenal, warning "this is a reality, not a threat".

Responding to Kim's comments, US President Donald Trump said "we'll see, we'll see" at his New Year’s Eve celebration, held at his Mar-a-Lago residence, in Florida.

'Atmospheric nuclear test'

Our correspondent said analysts were watching Kim's speech closely to see if he would mention an "atmospheric nuclear test".

"Weapons experts believe that North Korea has the capability to strike anywhere on the US mainland using an ICBM but they don’t yet believe that North Korea has yet the technology to miniaturise a nuclear warhead and mount it on a missile that can re-enter earth’s atmosphere intact," she said.

"To find out whether he has the technology to do so he would have to conduct such a test, but there was no mention of that."

North Korea said it had successfully launched a new ICBM capable of reaching the US mainland, the third test of its kind in 2017, on November 29.

The missile is the "most powerful ICBM" yet to be tested by the country, according to North Korean state television Korean Central News Agency (KCNA).

The UN Security Council imposed a fresh round of sanctions on North Korea in December following the test.

The latest sanctions, proposed by the US to prevent Pyongyang from furthering its nuclear weapons development, were the third set of restrictions imposed in 2017.

The US has said no diplomatic talks with North Korean can take place without a "full cessation" of the country's nuclear programme.