Kurbanguly Berdymukhamedov, the deputy prime minister, was made acting president with the Turkmenistan Security Council's backing after Niyazov's death.
The council, made up of ministers and other officials, took over the administration of day-to-day affairs in Turkmenistan last week after 21 years of Niyazov leading the country.
Stability in Turkmenistan is of strong interest to both the West and Russia. It has enormous natural gas reserves and occupies a geographically strategic position, bordering both Afghanistan and Iran.
Berdymukhamedov said last week that the presidential election would be held "on a democratic basis that has been laid by the great leader" - seen as an indication that Turkmenistan does not plan a pluralistic election.
Turkmenistan has only one legal political party - the Turkmenistan Democratic party - and opposition is suppressed.
Opposition leaders living abroad have said they intend to return to Turkmenistan in the wake of Niyazov's death, but have not succeeded.
Under the constitution, the People's Assembly sets an election date within two months of the president's death.
However, the body also has the authority to change the constitution.
Questions about how closely the constitutional procedures would be followed arose within hours of the announcement of Niyazov's death.
The constitution says the speaker of parliament was to become acting president, but the role was taken by the deputy prime minister, and a criminal case was opened against the parliament speaker.
Berdymukhamedov's unexpected rise to the acting president's post sparked speculation of an internal power struggle and that elections could be postponed until autumn.