Lawmakers today viewed a videotaped farewell address from Akaev, who fled to Moscow after protesters stormed his office 24 March.
But for the third-straight day, the deputies were unable to decide whether to accept Akaev's resignation.
The parliament canceled the date that had been suggested for the presidential election, 26 June, and reportedly planned to set a new date only after deciding Akaev's status.
Akaev signed a resignation agreement in Moscow on 4 April.
"Guided by my human and civil duty before my own people as well as by humanistic motives, I would like to declare my early resignation as president, based on my own request," Akaev said in the taped message.
A minority of lawmakers in the 75-member assembly have said they want to impeach Akaev rather than let him resign.
Akaev called his message "my final presidential message amid all the gravity and bitterness of words being said about my early resignation." He added that he had fled the country to prevent civil war, and stated his own aversion to using deadly force during the crucial hours when protests turned into a storming of the presidential and government buildings in the capital Bishkek on 24 March.
"My last order as president was the order not to shoot," Akaev said. "Again and again thinking over my actions in the critical situation of 24 March, I think that at the most difficult moment in my life, I made the only correct decision that meets genuine interests of the country and the people. By this I prevented a civil war. I have not stained my hands with blood of my countrymen, I didn't allow split of the country."
In the message, Akaev called his ouster after a nearly 15-year-rule a "national catastrophe." He said he is "sure history will consider the Akaev period as a bright era" and wished his successors success.
He also urged the country's political forces to ensure a democratic process in the upcoming presidential election.
"Guided with the highest interests of my people, first of all, I am calling on the Zhogorku Kenesh [Kyrgyz parliament] and all of the republic's healthy forces to hold the forthcoming presidential elections in a worthy and democratic [manner], in the spirit of the high principles of transparency, openness, and fairness, which have increasingly strengthened in the country's public and political life in the recent years," Akaev said.
In another development, Kyrgyzstan's Supreme Court today postponed a review of opposition leader Felix Kulov's appeal of an embezzlement conviction. The review was rescheduled for next week.
The court yesterday overturned a guilty verdict of abuse of office relating to when Kulov was Kyrgyz security chief.
Kulov needs both convictions overturned to allow him to run for president in elections set for 26 June.
Kulov has always maintained his innocence, saying the convictions were politically motivated.
(with reports from ITAR-TASS/AP/AFP/Reuters)[For more on events in Kyrgyzstan, see RFE/RL's dedicated Revolution in Kyrgyzstan webpage. For coverage of the region, see Central Asia in Focus]