During the 40-minute meeting, which was also attended by Assam chief minister Tarun Gogoi, a seven-member ULFA team led by its "chairman" Arabinda Rajkhowa presented the demands, contents of which were not available immediately.
However, sources said, ULFA has already given up its demand for a "sovereign state" and is likely to press for more autonomy, special status for Assam and other safeguards for the people there under the Constitution.
Gogoi described Friday's meeting as a significant step in bringing peace in Assam and said both state and central governments were sincere about finding a peaceful solution to the problem.
"If necessary, we may have to change law. But we must find a peaceful solution under the Constitution," he said.
The sources said the meeting will give fresh impetus to the peace process as the charter of demands will be the basis of the dialogue with the ULFA.
This will be ULFA's first formal peace negotiation with the government in its 32-year-old history. So far, only preliminary talks between the ULFA and Centre's interlocutor P C Haldar have been held in Guwahati.
Rajkhowa and others are understood to have asked the government to bring back its "general secretary" Anup Chetia, who is in detention in Bangladesh since 1997, to facilitate his participation in the peace talks.
"Anup Chetia should be brought back to India so that he can take part in the talks," Rajkhowa had said yesterday after reaching here.
Chetia is likely to be deported from Bangladesh as a major confidence-building measure ahead of Prime Minister Manmohan Singh"s visit to Dhaka early next month.
Rajkhowa had also expressed optimism about the dialogue process to bring a political solution to their demands.
Last month, the ULFA had issued a statement saying they will give up violence, suspend all operations and would like to begin talks.
Representatives of central and state governments and ULFA will take part in future meetings, the sources said.
Rajkhowa and other members of the group had "introductory" talks with Prime Minister Manmohan Singh and Chidambaram in February.
However, the group's elusive "commander-in-chief" Paresh Baruah has been opposed to any dialogue with the government if "sovereignty" issue is not on the table.