The prime minister assured the people of Nagaland that the Centre will always be sensitive to the needs of the people.
The parties agreed to the demand of tribal bodies and civil society groups to resolve the Naga political problem first.
Isak Chishi Swu and T Muivah will represent the Naga outfit; the government side is likely to include Oscar Fernandes, Prithviraj Chauhan and S Reghupaty.
'Operation Hurricane' was in progress in state's Tirap district bordering Myanmar.
Swu and Muivah, who are scheduled to reach New Delhi on Sunday night from Amsterdam, are expected to meet Home Minister Shivraj Patil on Monday, official sources said.
They were last here about a year ago.
The Centre's interlocutor for the Naga peace process, K Padmanabhaiah, is holding talks with National Socialist Council of Nagalim (I-M) in Bangkok for the second time since the Manmohan Singh government took over.
Let us end tensions that have sometimes existed between us and live as good neighbours, who respect each other's rights, the outfit said in a statement.
'The fact that NSCN leaders are here in India for talks is a very positive development,' says Mizoram Chief Minister Zoramthanga.
A huge crater was created at the site of the ambush and two vehicles -- a jeep and a Shaktiman truck --were completely damaged.
'Never before has an Indian politician made such huge electoral gains on dead bodies. For the moment, Vajpayee is speaking the language of the VHP-RSS,' says Praful Bidwai.
The talks should lead to an amicable settlement by establishment of a tripartite arrangement to accommodate Meitei, Naga and Kuki, the Kuki National Army said.
A joint statement signed by the two sides at the conclusion of their three-day talks said "both parties must work to maintain a peaceful and violence-free environment till then."
During its talks with the Centre, the NSCN (I-M) has demanded the formation of 'Greater Nagaland', which includes parts of Manipur.
Nagas have now a much better understanding with the people of India, NSCN (I-M) chairman Isak Chisi Swu said after meeting George Fernandes.
Although no accord is likely to be reached, the talks with the Indian leadership are expected to boost the efforts to bring peace to Nagaland, the sources said.
"We had very good but tough discussions. Both sides have agreed to extend the ceasefire by another year," Centre's emissary K Padmanabhaiah told PTI after three days of talks with NSCN (I-M) General Secretary T Muivah.
Khaplang died following a cardiac arrest.
The government will make this clear before reaching any agreement with the outfit, Padmanabhaiah said.
According to a statement by the Eastern Command, a column of the Indian Army operating along Indo-Myanmar border was fired upon by unidentified insurgents of the National Socialist Council of Nagaland-Khaplang about 4.45 am.
He said cross-border infiltration will continue because camps across the Line of Control, from where terrorists are launched, are still operational, and warned that the Indian Army is ready to "receive" them and keep dispatching them to their graves.
At least four militants belonging to two rebel groups were killed in Assam in two separate encounters with security forces on Wednesday morning.
People who had fled from the villages located close to the site of June 4 ambush on Armymen in Manipur's Chandel district have started to return home.