Constitutional reform was a key election promise of Evo Morales, Bolivia's first indigenous president, and he has billed the effort as a way to cement his reforms and empower the country's poor, indigenous majority.
The unofficial results gave Morales's Movement Towards Socialism (MAS) party 135 seats out of 255, far short of the two-thirds majority it needed for total control.
The vote, which also included a referendum on greater regional autonomy, was the president's first electoral test since he took office in January and he said the results showed backing for reforms such as nationalisation of the energy industry.
"This support ... gives us the strength to go on changing," Morales told state television. He said the result was a triumph for his government and for democracy.
In another part of the referendum, four of Bolivia's nine provinces backed gaining greater autonomy over central government.
Morales had campaigned for a "no" vote on the issue, saying it would benefit only the county's "oligarchs", and the "no" vote won 56% of the vote nationwide, projected results showed.
Morales has championed coca
Political analysts said Morales's "no" campaign could create conflict with the powerful pro-autonomy lobby of wealthy Santa Cruz province, an opposition stronghold.
State leaders there have complained that revenue is being siphoned off by the central government to subsidise the country's highlands.
It could also mean further bargaining with political opponents such as
the Podemos party of Jorge Quiroga, the former president.
Victor Hugo Cardenas, Bolivia's former vice-president, said: "The message is that the country wants a constitutional assembly driven by MAS, but not just by them. Their proposals will have to be agreed with other political parties."
Morales was elected president last December by a large majority and remains hugely popular in Bolivia.
He has nationalised the country's oil and gas industries, begun a wide-ranging land redistribution plan for peasant coca farmers and proposed free access to health care.