That 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.
Dmitry Babich, a political analyst with Russia Profile, told Al Jazeera:
"There are several groups that would like to come to power now.
"Turkmenistan is a very important country in terms of natural gas. It's a major supplier to the former Soviet Republics and Europe. Although the US, EU and Russia would like to see certain stability there, they would all like to put their man in charge.
"It remains to be seen what role Russia and the US will play.
"In the past Niyazov actually got more support from the US than from Russia."
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.