The agreement was reached after Central Election Commission chairman Sulaiman Imanbaev resigned, officially on health grounds. Imanbaev was replaced by Turgunaly Abdraimov.
Today, the new parliament set to work after electing opposition leader Omurbek Tekebaev as its speaker.
Yesterday's ruling runs counter to a Supreme Court decision made hours after Akaev was overthrown on 24 March to invalidate the results of those polls. That ruling automatically extended the mandate of the outgoing, bicameral legislature -- thus paving the way for an unprecedented constitutional crisis.
For the past five days, Kyrgyzstan has been effectively living with two competing legislatures -- the old parliament and the new, single-chamber parliament. To make matters more complex, a number of outgoing lawmakers were reelected earlier this year and hold seats in both parliaments.
It was this controversy surrounding the recent elections that sparked the wave of street protests that culminated in the storming of the White House last week. Yet, addressing members of the old parliament yesterday, opposition leader Feliks Kulov publicly lent support to the new legislature.
"Whether you like it or not, the new parliament must be chosen. Personally I don't like some of the deputies who have been elected to the new parliament. But, as a law-abiding citizen, I will respect the decisions of the new parliament. There is no other alternative," Kulov said.
Kulov's position is supported by demonstrators who still gather outside the White House -- as the headquarters of the government and presidential administration are known in Bishkek. The protesters blame Kyrgyzstan's new interim leader, Kurmanbek Bakiev, for allegedly relying on the old parliament, whose legitimacy they do not recognize.
It is that parliament which last week voted to make Bakiev interim prime minister and interim president -- a move Kulov said is anticonstitutional.
In a bid to remove this legal flaw, the new legislature today appointed Bakiev as prime minister -- thus legalizing his duties as interim president. The Kyrgyz Constitution says that, in the absence of the president, the prime minister assumes his duties.
Bakiev today denied there were fundamental disagreements between himself and Kulov over which parliament should be considered legitimate.
"Kulov says he supports the new parliament. I have already stated my position regarding the new parliament and I wouldn't say there is an argument [between us]. There are common points and I think that, in the nearest future, it will be clarified," Bakiev said.
Today, demonstrators gathered in front of the parliament building to express support for the outgoing legislature.
Addressing members of the old parliament the day before, Kulov blamed them for driving the country into deeper crisis by refusing to step down.
"On what grounds are going to call on people to oppose the new parliament? You have no grounds for [that] and people are not going to follow you. In accordance with the law, I will order the arrest of anyone who does this," Kulov said.
On 26 March, the upper chamber of the old legislature voted to extend its own mandate and that of the lower chamber until the early presidential elections set for 26 June.
It's not clear whether the Central Election Commission's decision to recognize the mandate of the new parliament would invalidate the 26 June vote.
Bakiev was scheduled to meet again with the upper chamber today to try to sort things out.
Meanwhile, 25 of the 60 members of the lower chamber of the outgoing parliament today voted to suspend their work and urged the upper chamber to do the same in order not to let the crisis deepen further.
It is unclear what legal effect the vote will have -- but it does prevent the lower chamber from meeting again since it will not have a quorum.
The Organization for Security and Cooperation in Europe (OSCE) has expressed concern at the Kyrgyz constitutional deadlock.
Addressing reporters yesterday in Bishkek, the personal representative of the OSCE chairman-in-office for Central Asia, Alojz Peterle, said his organization would assist the interim Kyrgyz leadership in finding a way out of the crisis.
"As far as constitutional affairs are concerned, you know that we have now two, we can say, two parliaments and this is a very, very sensitive issue. It is not only an issue for legal experts, it is definitely a sensitive political issue. I would like to tell you that efforts are going on in order to get as soon as possible three experts on constitutional and legal issues. I expect that at least two of them will be here in two or three days, because we think that the need for them is urgent," Peterle said.
The OSCE Bishkek mission head Markus Muller yesterday hinted that his organization would welcome a decision to defer the early presidential elections.
"For the organization of presidential elections -- for any elections -- you need a certain level of stability. And only with such a level of stability [these elections] should be organized, in my view," Muller said.
The fact that President Akaev has fled the country without resigning may create some legal problems that could be, in principle, solved through impeachment. But in the present situation, it remains unclear which legislature could initiate such a procedure.
Today, the speaker of the new parliament suggested another way to solve this problem. Tekebaev said a special commission should be set up to enter into talks with Akaev and convince him to return to Bishkek and tell the nation that he is stepping down:
"As I see this commission, it should also be tasked with contacting Askar Akaev, who is still formally president, and examine with him how [he could legally transfer his powers]. We must move the political process toward the law," Tekebaev said.
Kyrgyzstan's acting leader Bakiev has already said that he will participate in the electoral race. As for Kulov, he claims to have no political ambitions, although many in Bishkek believe he will eventually run for president.
Kulov was released from prison on 24 March, hours after the storming of the White House. He was serving a 10-year jail sentence on charges of abuse of power.
Yesterday, Kulov filed an appeal with the Supreme Court, demanding a new trial. A ruling to acquit the former security and interior minister would remove a major legal hurdle in case he would decide to run for president.
For more background on the crisis in Kyrgyzstan, see RFE/RL's dedicated website Revolution In Kyrgyzstan