Provisional results of a weekend referendum showed more than 70 percent of participants had approved two key amendments to the constitution.
The vote clears the way for an election to a new-style parliament, which Akayev hopes will be more accommodating to his liberal reforms.
The referendum means Akayev has succeeded in setting the stage to oust the Soviet-era parliament without violence.
The electoral commission said 86 percent of Kyrgyzstan's 2.2 million voters participated in the referendum.
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