The comments are a marked shift in tone from the isolated country after decades of animosity towards the US.
South Korea’s Yonhap news agency reported that senior diplomats from both countries were meeting on Monday to try todraft an agreement to present to their leaders.
North Korea’s state media does not usually report on the leader’s activities in real-time and the summit has only had a passing mention so far.
But the editorial in Rodong Sinmun confirmed that Mr Kim had travelled to Singapore to “establish a new relationship to meet the changing demands of the new era”.
It said “broad and in-depth opinions” would be exchanged to “establish a permanent and peaceful regime in the Korean peninsula and to solve problems that are of common concern, including issues to realise the denuclearisation of the Korean peninsula”.
“Even if a country had a hostile relationship with us in the past, our attitude is that if this nation respects our autonomy…we shall seek normalisation through dialogue,” it reads.
Denuclearisation has been the central issue in the run-up to the talks. The US wants North Korea to give up its nuclear weapons, but North Korea is widely expected to resist that and it is unclear what it might ask for in return.