Naga rebel leaders meet Sonia Gandhi
Thousands have died in the fight for a homeland for Nagas in India's troubled north-east.
The Naga insurgency was India's first ethnic rebellion.
Indian Prime Minister Manmohan Singh has promised to seek a settlement that would ensure dignity for the Naga people after 50 years of conflict.
Mr Swu and Thuingaleng Muivah had paid a short visit to Dimapur three years ago after spending 30 years in exile but this is their first major homecoming after they went underground in the 1960s.
The BBC's eastern Indian correspondent Subir Bhaumik says the visit will give both leaders a chance to get a sense of the situation on the ground, after spending so much time away from their homeland.
Hundreds of rebels joined in welcoming the leaders on Tuesday along with some 50 Naga tribal and clan representatives clad in traditional dresses.
Dimapur was decked up with colourful banners and flags of the rebel group.
"The NSCN flag is all over Dimapur. Looks like the rebels have taken over the town," local journalist Pradeep Pareek told the BBC.
The two leaders told journalists that they would spend a month in Nagaland and discuss their ongoing negotiations with the Indian government.
The two sides have been engaged in talks for the past seven years but have failed to reach accord.
Other Naga separatist factions have said that the NSCN alone was not in a position to negotiate on behalf of the Nagas.
In a related development, the Burmese army has claimed that it has destroyed "almost all the camps" belonging to a NSCN faction inside its territory during a major two-week-long offensive
The Khaplang faction of the NSCN has admitted to loosing several bases during the Burmese offensive.
The attacks coincide with a month-long drive by about 6,000 Indian troops against rebels in the north-eastern Indian state of Manipur.
The NSCN wants a greater Nagaland comprising Naga-inhabited areas of the neighbouring states of Manipur, Assam and Arunachal Pradesh.
These states are vehemently opposed to the idea, and correspondents say it is a major sticking point in negotiations between the Naga rebels and Delhi.