Only 153 of the assembly's 255 delegates - most from the ruling Movement Toward Socialism party (MAS) - joined the session.
Seven delegates from the National Unity party were almost the only opposition presence.
Hundreds of changes
More than 400 changes to the constitution were approved on Sunday.
|"We're coming to a happy ending, we're managing to approve |
the new constitution the Bolivian people are asking for"
Roman Loayza, Movement Toward Socialism party
But in an apparently political move that will make it easier to get the entire text ratified in the assembly early next year, one article dealing with the definition of unproductive land holdings was left to be put to a national referendum.
After that article has been approved, the assembly will vote again, before another referendum is required on the full constitution.
Roman Loayza, head of the MAS delegates in the assembly, said: "We're coming to a happy ending. We're managing to approve the new constitution the Bolivian people are asking for."
The assembly's work was stalled for months because of the fear of violence against delegates, but two weeks ago it met under military guard in Sucre and approved an outline of the constitution in a vote boycotted by the opposition.
Three people died in protests after the vote causing Sunday's assembly to be moved to Oruro, 230km south of La Paz.
Miners guard session
Miners loyal to Morales guarded the university auditorium where the session was being held, exploding small dynamite charges occasionally to intimidate any potential anti-assembly protesters.
Morales says that the changes will redress centuries of discrimination by a political class dominated by a European-descended elite.
It will hand 62 per cent of the population more control of their traditional lands and turn the bicameral legislature into a one-house body.
Morales became Bolivia's first leader of indigenous descent in January 2006, ending the political dominance of a mainly white economic elite.