A four-member delegation of the armed group departed from Bangkok for the Myanmar capital Yangon on Wednesday and is expected to return early next week, said KNU spokesman Phado Mahn Sha in the Thai border town of Mae Sot.
Phado Mahn Sha said contacts between the two sides resumed after a year-long impasse after the regime dispatched its representatives to meet with KNU officials at Mae Sot on 22 November.
KNU and Thai intelligence sources said the Yangon talks were arranged after progress was made on a number of issues, including an agreement that no third country would be involved in the negotiations.
Under the deal, all the talks must be conducted inside Myanmar territory, either in border towns or the capital, and the opposition National League for Democracy led by Aung San Suu Kyi is to be excluded.
"There is regular contact going on with the KNU and the way has always been open for them to come into the ceasefire"
labour minister, Myanmar
The government also agreed to the KNU's demand that they negotiate a ceasefire first before surrendering their weapons - an issue which caused previous talks to end in failure.
Myanmar's Labour Minister Tin Win confirmed that peace negotiations were underway between the two sides.
"There is regular contact going on with the KNU and the way has always been open for them to come into the ceasefire," he said in Yangon.
However, he would not comment on whether the peace push was linked to the regime's "road map" towards democratic reforms under which it is attempting to involve ethnic groups in a national convention to write a new constitution.
The KNU is one of few remaining armed groups fighting an independence campaign against the military government in Yangon. The junta estimates there are 7,000 fighters in the insurgent group.