"The interim government is in charge," said former foreign minister Roza Otunbayeva, who was named the head of the interim government.
"This composition of the political system will function for six months, during which time a new constitution will be written and presidential elections will be organized in accordance with all democratic norms."
She also said that her interim government “insists that [President Bakiyev] stands down”.
Bakiyev’s location was not immediately clear after he fled the capital of the Central Asian state Wednesday. On Thursday he told Russian radio that he was in southern Kyrgyzstan. Reports have put him in the south, near Osh, his traditional stronghold.
Bakiyev said in a statement published by the local news website 24.kg, considered to be the online mouthpiece of his administration, that he had no plans to step down.
"I declare that as president I have not abdicated and am not abdicating responsibility," he said, adding that the country was on the edged of a "humanitarian catastrophe" and admitting he no longer had control over the army and police.
Demonstrations in Bishkek Wednesday turned violent when security forces fired live bullets into a crowd of between 3,000 and 5,000 people who were overturning cars and setting them on fire.
At least 75 people were killed in the riots, according to the health ministry, though a senior opposition figure told the AFP news agency that the death toll was more than 100.
Opposition protesters took over the government administration Wednesday night and announced on state radio that they had formed a provisional government.
The capital was calm Thursday after a day of violent protests followed by looting.
“The looting is over for the time being," Paul Quinn-Judge, Central Asia project director of the International Crisis group, told RFI from Bishkek. Most of the large shops in the city centre have been trashed, as have many government buildings and other locations associated with Bakiyev.
Quinn-Judge says that the centre of the capital is still full of people from outside the city who came in for Wednesday's demonstrations, who are "clearly staying around, and probably don’t have too much else to do, other than have another go at looting tonight.”
However, outside the city centre, things are things are “pretty normal”, despite the difficulty of buying food.
Otunbayeva and the new government have a daunting task ahead of them, says Quinn-Judge.
“This country is in a terrible mess: the infrastructure is crumbling; many things will stop operating in the new future, and the new regime will be the people who will be at the switches when this happens," he said.
"Therefore they have been very fast to start saying to people: this is our problem, this is what’s going to happen, this is why it’s going to happen, and this is why we need your help.”
He says the future now depends on “intelligent leadership, and a quick, well thought out strategy by the new leaders.”
Otunbayeva has been trying to secure Russian support. She spoke on the phone with Russian Prime Minister Vladimir Putin on Thursday. Putin’s spokesperson told the AFP news agency that the president was “ready to provide necessary humanitarian aid to the people of Kyrgyzstan.”
An opposition leader, Omurbek Tekebayev, told a group of supporters about the conversation, saying that Putin "supports the policies of Kyrgyzstan's provisional government”.
Russia has denied accusations that it was involved in supporting the opposition to overthrow the government.
President Dmitry Medvedev said in a statement that the situation was “Kyrgyzstan's internal affair, but the form the protest took showed ordinary people's extreme outrage at the existing regime."
Russia and the US both have military bases in the country, which is seen as a strategic point between China, Russia and southwest Asia.
Otunbayeva said that a US airbase outside Bishkek that is key to transporting troops, fuel and weapons to the Nato campaign in Afghanistan would remain open.