He told BBC Russian he was in southern Kyrgyzstan but would not disclose the exact location.
Mr Bakiyev said he was the legitimate president and condemned the uprising, saying "armed people are strolling the streets of the capital - stealing things, looting and pillaging, killing people. And this new 'interim government'... is completely incapable of imposing order - and they're simply blaming the president for everything."
But he added: "If this so-called 'temporary' government that has appointed itself is prepared to begin negotiation talks, then I'm prepared to listen to them."
In an earlier interview with Russia's Ekho Moskvy radio station he insisted he had "no plans" to leave Kyrgyzstan but admitted: "I don't have any real levers of power."
AT THE SCENE
Rayhan Demytrie, BBC News, Bishkek
With the exception of riot police who clashed with protesters near the offices of Mr Bakiyev on Wednesday, the police presence has been almost non-existent in Bishkek over the past two days.
In a small cafe, away from the city centre, I found a group of policemen in their uniforms chatting and smoking cigarettes. "We had no orders to act," one officer said. Most of the policemen even appeared to sympathise with the protesters.
After two days of mass protests, a night of widespread looting and constant gunfire, there is sense of chaos and uncertainty in Bishkek.
Mr Bakiyev's defiance followed a news conference held by Ms Otunbayeva in which she said her interim government - which would remain in power until elections are held in six months - was fully in control of the country and had appointed new ministers.
She said Mr Bakiyev was trying to rally support in his home region of Jalal-Abad and urged him to resign, saying: "His business here is over."
Ms Otunbayeva went on: "What we did yesterday was our answer to the repression and tyranny against the people by the Bakiyev regime.
"You can call this revolution. You can call this a people's revolt. Either way, it is our way of saying that we want justice and democracy."
The violence initially broke out in the provincial town of Talas on Tuesday and spread to Bishkek, where demonstrators marched on government buildings, and another town, Naryn, on Wednesday.
The opposition claim to be in control, but you can tell that there's no law and order. Our opposition is so weak, nobody believes them
Ms Otunbayeva said the "status quo would remain" regarding the bases but that some questions had to be considered.
She also thanked Russia for its "significant support" and said she would be sending envoys to Moscow for talks.
Later another opposition leader, Omurbek Tekebayev, told Reuters that Russia had "played its role in ousting Bakiyev" and that there was a "high probability that the duration of the US air base's presence in Kyrgyzstan will be shortened".
Russian Prime Minister Vladimir Putin and Ms Otunbayeva have already held telephone talks. An extra 150 paratroopers are being sent to Russia's Kant military base, near Bishkek.
Moscow has denied playing any role in the unrest.
In his Russian radio interview, Mr Bakiyev said the uprising would not have been possible "without outside interference". He refused to say which country might have been involved.
US President Barack Obama's adviser on Russia, Michael McFaul, insisted this was "not some anti-American coup".
A US envoy met Ms Otunbayeva late on Thursday in Bishkek, the state department said, and called for calm and the respect of "democratic principles".
KEY LOCATIONS IN KYRGYZ UPRISING
Bishkek: Opposition claim to have control. Protesters still surround government HQ (aka the White House) which has been ransacked and part of it set on fire. Reports of looting in the city.
Osh: President Bakiyev has a support base in the country's second city and is believed to be in Jalal-Abad.
Naryn: Second day of unrest. New opposition governor installed.
Talas: Uprising began here on 6 April. Interior minister beaten up by protesters on 7 April who stormed police HQ and installed new governor.
Border with Kazakhstan is closed.
"Limited operations" at US military base in Manas.
Are you in the area? Have you been affected by the events? If you have information you would like to share with the BBC, please contact us using the form below
Send your pictures to firstname.lastname@example.org or text them to +44 7725 100 100. If you have a large file you can upload here.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.