Berdymukhamedov said: "Turkmenistan will continue the policy of neutrality based on the principle of good neighborliness and mutual respect."
"We will continue to go the political course of the great leader and will implement the domestic and foreign policy course of Turkmenistan's first president, which is based on peace-loving and humanism."
Berdymukhammedov said the country's Popular Council, made up of more than 2,500 Turkmen officials, would meet on Tuesday to set a date for a presidential election and introduce presidential candidates.
Turkmenistan in mourning
Turkmenistan's government held an emergency meeting on Thursday, naming Berdymukhamedov, the deputy prime minister, to head a commission handling the president's funeral.
According to the constitution, parliamentary president Ovezgeldy Atayev was due to take over in the interim, but that plan was modified after legal proceedings were suddenly brought against him on Thursday.
The government announced that the country "must remain united" and would respect its international obligations and bilateral treaties.
A statement read out on state televison said: "The internal and external policies proclaimed earlier will be continued further."
Niyazov had undergone heart surgery in 1997 and last month he publicly acknowledged for the first time that he had a heart condition.
Niyazov, who styled himself Turkmenbashi, had ruled Turkmenistan since 1985, establishing a personality cult with hundreds of statues and golden busts of himself erected throughout the country.
He also renamed several months and days in the calendar after himself and his family and ordered a number of "outlandish" projects, including the creation of a man-made lake in the Kara Kum desert, an ice palace outside the capital, a ski resort and a 130ft pyramid.
Earlier this year he announced he would provide citizens of Turkmenistan, which is the second-largest natural gas producer in the former Soviet Union after Russia, with natural gas and power for free through to 2030.
On Thursday, Turkmenistan's state television showed Niyazov's portrait in a black frame while a news presenter read a list of his accomplishments.
In the capital, Ashgabat, workers removed holiday decorations and New Year's trees, and liquor shops were ordered shut.