The announcement, which included a government statement, said Niyazov died of a cardiac arrest at 1:10 a.m. local time (8:10 p.m. GMT Wednesday) at the age of 66.
The embassy official said over the phone that the TV channel showed Niyazov's portrait in a black frame as the statement was read out.
"The television channel is recounting the president's biography and what he has done for Turkmenistan and the international community," the Russian diplomat said.
The TV broadcast included an official statement from the Turkmen government, the State Security Council and parliamentarians.
"The people of Turkmenistan ... will remain committed to the political course of Saparmurat Turkmenbashi," the statement said.
Niyazov ruled the energy-rich ex-Soviet Central Asian republic for 21 years with an iron fist and created a personality cult styling himself as Turkmenbashi, or head of the Turkmen people.
The late president had been suffering from heart problems for several years. In 1997 he underwent heart bypass surgery in Germany. Since then, German cardiologists had traveled to Turkmenistan regularly to treat the leader.
Leaders of the opposition, who have been living abroad to avoid prosecution, have said they might meet in the next few days to discuss the situation following the president's death.
Khudaiberdy Orazov, a former deputy prime minister and chairman of the Vatan movement, said he had already spoken with other opposition leaders over the phone.