Bakiyev fled to neighboring Kazakhstan on Thursday, ending days of turmoil that disrupted US military flights through a Kyrgyz air base to operations in Afghanistan.
The crisis has underlined rivalries between the United States and Russia for influence in Central Asia, a vast region between China, Afghanistan and the Caspian Sea.
The interim government, led by Roza Otunbayeva, said Bakiyev had faxed his resignation letter overnight from Kazakhstan.
"I tender my resignation in these tragic days as I understand the full scale of my responsibility for the future of the Kyrgyz people," Bakiyev said in the letter.
Otunbayeva's chief of staff, Edil Baisalov, later presented the original, written in large, jagged letters, to reporters and said it was delivered to the interim government by Kazakhstan's ambassador in Bishkek.
Bakiyev's departure has sharply reduced tensions in the impoverished former Soviet republic after a violent uprising against his five-year rule raised the spectre of civil war.
He has not appeared in public since fleeing. Officials say he is in the Kazakh city of Taraz with his wife and two children. Russian media say he could fly on to Turkey or Latvia.
Taraz, a sleepy town in the southern Kazakh steppe on the Kyrgyz border, overflowed with rumours after Bakiyev's arrival.
A local security source said Bakiyev had been whisked to a secret location in Taraz and locals saw a motorcade of jeeps without number plates driving out of the airport overnight.
At least 84 people were killed in the uprising last week when a protest against Bakiyev's rule erupted into a night of gunfire and looting in the Kyrgyz capital. Troops loyal to Bakiyev shot into a crowd of thousands of demonstrators.
Addressing the nation in a live televised statement, Otunbayeva said Bakiyev must stand trial over the events.
"Retribution is unavoidable. Justice will prevail," she said.
RUSSIA VS US Otunbayeva said the presidents of the United States, Russia and Kazakhstan - which holds the rotaing chair of the Organization for Security and Cooperation and Europe - personally had helped mediate in the crisis.
Kazakh President Nursultan Nazarbayev, speaking in the capital Astana, made no mention of Bakiyev's whereabouts and urged the new government to restore control over the country.
"The authority is weak on the ground and this is fertile ground for various bandits and criminal gangs," he said.
"So I wish for the interim government to stabilise the situation in the country first of all and to take power into their hands." Russia, which also has an air base in Kyrgyzstan, sought to pressure Bakiyev to evict the United States from its Manas air base, through which 50,000 US troops passed last month.
The new government says it plans to allow Washington to keep the base but has hinted it may review some elements of its work.
Speaking in Brasilia, Russian President Dmitry Medvedev, who had warned that Kyrgyzstan could become a "second Afghanistan,” said he believed the "negative scenario" had been avoided.
China, the other major power with an interest in Kyrgyzstan, has said little in the week since the uprising in the neighboring state, but broke its silence on Friday with a foreign ministry statement supporting the new government.
Interim government officials said forces were conducting an operation in southern Kyrgyzstan to round up any Bakiyev allies thought to be hiding in the region. Bakiyev's defense minister has already been arrested, Otunbayeva said.
Bakiyev had demanded that two of his brothers, accused by the opposition of playing a role in the deaths of his opponents and last week's violence, should be allowed to leave with him. It is unclear where they are.
