Violence initially broke out in the provincial town of Talas on Tuesday and spread to the capital Bishkek, where demonstrators marched on government buildings, and another town, Naryn, on Wednesday.
Mr Bakiyev, who came to power in a revolution in the central Asian state five years ago - reportedly flew out of the capital on Wednesday to travel to the city of Osh in his home region of Jalalabad.
A statement attributed to Mr Bakiyev that appeared on the 24.kg news website quoted him as blaming the opposition for the violence and saying he would not resign.
Reuters news agency reported scuffles in Osh on Thursday between hundreds of Bakiyev supporters and members of the opposition who had taken over a government building.
AT THE SCENE
Richard Galpin, BBC News, Bishkek
Looting continues here in the capital, particularly of the offices of the President Kurmanbek Bakiyev.
The leaders of the opposition have moved quickly to announce that they are now in control after setting up what they call a temporary popular government until fresh elections can be held.
They say the armed forces are now under their command. But the president has not resigned, raising fears there could be further violence if he manages to mobilise his supporters.
All this will particularly worrying for the US military, which relies on a large air base near the Kyrgyz capital to send troops and supplies into Afghanistan.
At a news conference, the head of the interim government said it would meet with American diplomats to discuss the air base, but stressed it needed time to decide what it is going to do.
The scene in Bishkek on Thursday was calm, with the opposition apparently in control of the government headquarters.
There was widespread looting and gunfire during the night in the capital.
Speaking at a packed news conference, Ms Otunbayeva said an 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 the south 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 BBC's Rayhan Demytrie in Bishkek says Mr Bakiyev has a large support base in the south but it remains to be seen how many people there will turn out for him and whether he will try to fight back with their backing.
Kyrgyzstan is a strategically important central Asian state and houses a Russian base and a key US military base that supplies forces in Afghanistan. The US suspended military flights on Wednesday.
Ms Otunbayeva said the "status quo would remain" regarding the bases but that some questions had to be considered.
Ismail Isakov, named interim defence minister, has affirmed that the country's armed forces and border guards are under the control of the interim government.
On Thursday, UN Secretary General Ban Ki-moon said it was "time to work urgently in establishing constitutional order" in Kyrgyzstan.
TIMELINE: KYRGYZSTAN UNREST
March 2005: Protests over disputed parliamentary election, dubbed the Tulip Revolution, lead to fall of President Askar Akayev; Kurmanbek Bakiyev appointed acting president and PM
July 2005: Mr Bakiyev elected president by a landslide
May 2006: Mass protests demand constitutional reform and more action to combat corruption
October 2007: Referendum approves constitutional changes, which the opposition present as a step towards authoritarianism
December 2007: Mr Bakiyev's Ak Zhol party wins parliamentary poll; opposition left with no seats
July 2009: Mr Bakiyev re-elected in vote criticised by monitors
January 2010: Opposition leader Ismail Isakov jailed for eight years for corruption, sparking opposition hunger strikes
April 2010: Clashes between police and anti-government protesters leave 65 dead
Announcing he would be sending a UN envoy to the country immediately, Mr Ban said: "There are difficult social and economic issues underlying the unrest."
Russian Prime Minister Vladimir Putin and Ms Otunbayeva held telephone talks, Moscow said.
"It is important that the conversation was held with her in her role as the head of the government of national trust," Mr Putin's spokesman Dmitry Peskov told Reuters.
The Russian chief of staff of the armed forces said an extra 150 paratroopers were being sent to Russia's Kant military base, near Bishkek, to ensure the security of Russian personnel there. Moscow has denied playing any role in the unrest.
The United States said it deplored the violence and urged "respect for the rule of law".
On Thursday, European Union foreign affairs chief Catherine Ashton said the EU was offering emergency humanitarian aid to help stabilise the nation.
"I call on all sides to show continued restraint. A rapid return to public order is essential to avoid further loss," she said.
A Chinese foreign ministry statement said it was "deeply concerned" about events in Kyrgyzstan, which shares a 533-mile (858km) border with China, and hoped order could be restored soon.
Mr Bakiyev, 60, came to power amid a wave of street protests in 2005 known as the Tulip Revolution, but many of his allies have deserted him claiming intimidation and corruption.
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 the region.
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.
Flights suspended from US military base in Manas.
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