The opposition announcement came after Kurmanbek Bakiyev, the president, fled the capital Bishkek amid violent clashes between anti-government protesters and riot police on Wednesday.
But Bakiyev released a statement on Thursday saying that he would not resign.
"Today Kyrgyzstan is on the brink of a humanitarian catastrophe," he said in the statement on the news website, 24.kg, the AFP news agency reported.
"I declare that as president I have not abdicated and am not abdicating responsibility," he added.
Reports said that Bakiyev is currently in the southern city of Osh.
"We can confirm that the president has left the capital and has gone south to his heartland," Al Jazeera's Robin Forestier-Walker, reporting from Bishkek, said.
"We also understand that the prime minister has resigned and he was escorted safely from the White House, which is the Kyrgyz presidential administration building in the centre of the capital."
On Tuesday, thousands of people in the northwest town of Talas stormed regional government offices.
The protesters broke into a government building where they briefly took hostage Bolotbek Beishenbekov, the local administrator.
But Wednesday's violence was the deadliest with the health ministry saying that at least 75 people had died and more than 1,000 were injured in clashes between the police and protesters.
Toktoim Umetaliyeva, an opposition activist, however, said at least 100 people were killed by police gunfire during the day.
The unrest followed rising tensions between the opposition and Bakiyev's government, which they accuse of cracking down on independent media and fostering corruption.
Forestier-Walker said the protesters' grievances were a mixture of political and economic frustrations.
Recent widespread anger over the 200 per cent increase in electric and heating bills unified opposition factions and galvanised support for them.
Al Jazeera's Robin Forestier-Walker reports
on the deadly clashes in Bishkek
Many of Wednesday's protesters were men from poor villages, including some who had come to the capital to live and work on construction sites.
Already struggling, they were outraged by the high cost of energy and were stirred up by opposition claims of official corruption.
Bakiyev had promised to reform the country when he came into office five years ago, after street protests led to the country's so-called Tulip Revolution which ousted Askar Akayev, his predecessor.
Bakiyev gave his relatives, including his son, top government and economic posts and faced the same accusations of corruption and cronyism that led to the ouster of Akayev.
Opposition activists say they have routinely been subjected to physical intimidation and targeted by politically motivated criminal investigations.
Meanwhile, contradicting earlier calls by the opposition for the closure of a US air base outside the capital, Otunbayeva said that the interim government would keep the existing agreement with Washington.
"Its status quo will remain in place. We still have some questions on it. Give us time and we will listen to all the sides and solve everything," she said.
The base is in Manas outside the capital and serves as a transit point for supplies to the war in Afghanistan.
|Otunbayeva, the interim government leader, said she fully controls the country [Reuters]
A US military official in Washington said that some flights were briefly diverted at the base but it was never closed and scheduled troop movements in and out of Afghanistan were not affected.
Opposition leaders earlier said that they want the base closed because it could put their country at risk if the US becomes involved in a military conflict with Iran.
Russia has opposed the basing of US troops on former Soviet turf and would also be pleased with the closing of the base.
"Russia has not had a hand in the uprising," Vladimir Putin, the Russian prime minister, said at a news conference in Smolensk. Putin also called for calm amidst the unrest.
Putin talked with Otunbayeva by phone in her capacity as the head of the new government, Putin's spokesman said.
"It is important that the conversation was held with her in her role as the head of the government of national confidence," Dmitry Peskov, Putin's spokesman, said.
"Otunbayeva said she fully controls the situation in the country."