In response, the US has urged Turkmenistan to hold a "free, fair and open election" to replace the late Saparmurat Niyazov, an authoritarian who ruled the country for 21 years.
Gonzalo Gallegos, a spokesman for the state department, said: "We [the US] want Turkmenistan to have the most representative government possible.
"We would like to see a free, fair and open election that meets international standards and for the new president to be ready and willing to represent the aspirations and protect the fundamental rights of all people of Turkmenistan."
The former Soviet republic, strategically placed between Iran and Afghanistan, is believed to have the world's fourth-largest natural gas reserves, which provide a vital energy source for Europe.
The law, which was adopted by the people's council on Tuesday, said that the candidates' meetings with voters must be organised by local authorities, signalling that they will be subject to official control.
Meanwhile, the interim leader and presidential candidate, Gurbanguli Berdymukhamedov, who has emerged as Niyazov's heir apparent, said all the candidates must be provided with "all conditions for a successful campaign and guaranteed equal rights and opportunities".
The other five candidates are little-known officials.
Berdymukhamedov is seen as a likely presidential successor, after the people's council - a 2,500-strong assembly of hand-picked officials and elders - amended the constitution to allow him to run and unanimously backed his candidacy.
During Niyazov's rule, Turkmenistan became isolated from the outside world.
When Niyazov died last week of a heart attack, there were concerns that a power vacuum or struggle over succession could disrupt gas supplies.