The statement rejects allegations of widespread fraud in the 27 February and 13 March polls. But it quotes Akaev as saying the matter should be probed in those regions where election results have sparked the most controversy.
The apparent concession came after Akaev met with Central Election Commission Chairman Sulayman Imanbaev and Supreme Court Chairman Kurmanbek Osmonov.
Opposition leaders and many international observers have described the parliamentary vote as deeply flawed. The elections handed pro-presidential forces a commanding majority in the new legislature.
Scattered protests broke out in a number of Kyrgyz cities after the second round, with opposition leaders demanding that the results be nullified and that new elections be held. Protesters have also insisted that Akaev should step down as president.
On 21 March, opposition leader Roza Otunbaeva said Akaev's adversaries remain firm in their demands. "As of now, there is nothing to negotiate about [with the government]. We are demanding that the president resign," Otunbaeva said.
Otunbaeva made her comments shortly after reports emerged that protesters had taken control of the regional government headquarters in Osh, a southern city with a large ethnic Uzbek population.
The occupation in Osh came just hours after protesters managed on 21 March to retake the mayor's office in nearby Jalal-Abad.
Kyrgyzstan's AKIpress news agency reported on 21 March that demonstrators had also taken control of Jalal-Abad's airfield, piling stones on the runway to prevent the central government in Bishkek from flying in police reinforcements.
There were no immediate reports of fighting between security or police forces and protesters, although unconfirmed claims from the opposition suggested that injuries have occurred.
Jusupjan Jeenbekov chairs the Jalal-Abad People's Council, an alternative body set up by protesters. Talking to RFE/RL's Kyrgyz Service late on 20 March, he said police had shot at demonstrators, wounding three of them.
"Three people have been injured by police shots," Jeenbekov said. "One was injured in the neck, another in the leg, and a third on the hand. One of them had to be sent to hospital. The condition of the other two is fair, and they remained with [the protesters]," Jeenbekov said.
Reports that four Jalal-Abad policemen were beaten to death by angry protesters could not be independently confirmed. The government has denied that any violence took place.
Speaking on national television on 21 March, State Secretary Osmonakun Ibraimov said authorities have nothing to hide from citizens. Ibraimov pledged to report any casualties among either protesters or law-enforcement agents.
In comments broadcast on Georgian television on 21 March, opposition leader and former Foreign Minister Otunbaeva said no one was killed or wounded during the storming of the Osh administration headquarters.
"No one was killed," Otunbaeva said. "Everyone is safe. The people have taken control of the [city] administration without a single bullet being fired, without a single drop of blood being shed. The people's power has been established."
Otunbaeva said many policemen in both cities had donned civilian clothing and sided with the protesters. Her claim could not be independently confirmed.
In subsequent comments to RFE/RL's Kyrgyz Service, Otunbaeva warned that the protest movement would now spread to other towns and cities: "Nearly half of [Kyrgyzstan] -- the south -- is already under our control. We will move forward."
Law-enforcement officers kept a low profile as thousands of protesters wandered the streets of Osh and Jalal-Abad on 21 March. The Kyrgyz government has denied opposition claims that protesters control both cities. Also, authorities in the capital Bishkek dismissed reports that demonstrators have seized the Osh television station.
Meanwhile, the situation in other Kyrgyz areas was reportedly calm.
Addressing reporters in Bishkek, former Prime Minister Kurmanbek Bakiev suggested President Akaev could resolve the crisis by entering into talks with his opponents.
"What should be done to find a way out of the situation? Perhaps our president, Mr. Akaev, has to ripen for talks with the opposition to resolve that tense situation?" Bakiev said. In subsequent comments, Bakiev said he fears government troops will provoke violence against the demonstrators.
"I know, the authorities will now try to provoke bloodshed, God forbid, and then they will blame it on members of the opposition," Bakiev said.
Akaev has repeatedly warned that any attempt at emulating recent political upheavals in Georgia and Ukraine could drag Kyrgyzstan into civil war.
He let it be known on 21 March that he is not fundamentally opposed to meeting the protest leaders.
Speaking live on national television, presidential spokesman Abdil Segizbaev said talks involving Akaev are possible. He raised the possibility of the Kyrgyz president going to Osh and Jalal-Abad, "if protesters calm down and coolly assess what has happened."
Also on 21 March, Prime Minister Nikolai Tanaev said authorities will seek a negotiated solution to the crisis.
Photo Gallery: How The Protests Unfolded
Authorities Attempt To Contain Protests, Negotiate
Kyrgyz Police Battle With Protesters In Southern Cities
For more on the Kyrgyz elections, see RFE/RL's dedicated website Kyrgyzstan Votes 2005