The army claims its actions are in self-defense, a response to the Kachin blocking the road. They have seized at least one of the guerrillas' hilltop posts by the road.
The United States, China and the United Nations have all urged a peaceful resolution to the conflict, but so far there seems to be little momentum toward negotiations.
The 88 Generation Students, a pro-democracy activist group, visited the Kachin headquarters in Laiza on a self-appointed mission last week to encourage peace talks between the government and the rebels and to donate relief supplies for Kachin displaced by the fighting.
The group said the Kachin guerrillas' deputy commander, Gwan Maw, had asked it to help repatriate 27 Myanmar government prisoners of war, an offer it claimed the government had not yet responded to.
A novel effort to promote peace talks was suggested by a Member of Parliament from Myitkyina who had been telecommunications minister under the former military government and a member of the government team to negotiate with armed ethnic groups under the current government.
According to Myanma Ahlin and other state newspapers, Thein Zaw proposed in Parliament on Friday that since the military tensions make it difficult for the two sides to engage in face-to-face talks in Kachin state, they instead hold "a transparent electronic online discussion."
While Myanmar's Internet infrastructure is shaky, especially in remote areas, the proximity of the Kachin headquarters to the border with China means its leaders could use Chinese telecommunications links.