Electoral officials said more than 93 percent of those who voted approved of the proposed changes. Voter participation was reported at 65 percent.
The opposition, which before the referendum had called for a boycott, said the figures were rigged.
The Council of Europe said the referendum yesterday was marred by "serious abuses." The council said its 14 observers witnessed instances of fraud, secrecy, and the stuffing of ballot boxes.
Lord John Tomlinson, a member of the council's mission, said observers believed the official figures were inflated.
"The extremely low voting activity did not correspond to the high figures provided by the electoral commissions," Tomlinson said.
Figures are crucial because the constitutional amendments will take effect only if backed by one-third of eligible voters and 50 percent of those who actually cast their ballots.
If passed, the constitutional amendments will, among other things, transfer some presidential powers to parliament and the government.