Legally, Akaev must resign in the parliament. Deputies would then vote on holding new presidential elections. But early elections have already been called for 26 June.
Cholpon Baekova, the head of Kyrgyzstan's Constitutional Court, said today that vote will be held regardless of whether Akaev resigns or not.
"The election will be held in any case. At least [the individuals] who held a meeting today in the Constitutional Court discussed this question and clearly stated that the elections will be on 26 June, regardless of any announcement [by Akaev]," she said.
Akaev had earlier signaled a willingness to step down, but only under certain conditions. He outlined his terms during an interview yesterday with RFE/RL's Kyrgyz Service, Radio Azattyk:
"I am not asking anything above the law. First of all, I am asking that I and members of my family get security guarantees," Akaev said. Also, I am asking that the laws are observed. [The rules governing the status of ex-presidents] are written into the constitution. The upper house [of the old parliament] passed a law [on ex-presidents]. That is all I am asking for."
Akaev also wants his personal security to be guaranteed in Kyrgyzstan.
Kyrgyzstan's interim foreign minister, Roza Otunbaeva, said the new leadership is unable to offer valid security guarantees. She said yesterday Akaev might become the target of angry crowds if he returns to Kyrgyzstan.
Otunbaeva also said authorities are planning to seize property held by Akaev and his circle of family and friends. Such property, she said, was "plundered" from the Kyrgyz people.
Kirill Koktysh, an analyst with the Moscow Institute of International Relations, said that Akaev is in a poor negotiating position because his power has collapsed.
Akaev fled the country after protesters stormed government buildings on 24 March. Now, Koktysh said, the new parliament and interim government do not have sufficient control over the country to guarantee his safety:
"I don't think the parliament has enough control over the situation. It can decide whatever it wants, but the problem is how to enforce such a decision," he said.
Koktysh said it appears that most of the demonstrators were protesting Akaev's corruption and nepotism. He said much of the looting that followed the storming of the government complex was directed at shops owned by Akaev's relatives.
Koktysh said there are many Kyrgyz who do not want to see Akaev back in the country. "There are many people who are unhappy with Akaev. And nobody has a burning desire to risk one's own life for the sake of Akaev's safety," he said.
Koktysh said legally, Akaev is still president. But he does not have the power or the popular support to continue being one.
"According to the law, he is still the president. But society has already refused to continue thinking of him as a president," Koktysh said. "They don't consider him one now."
All that remains now, Koktysh said, is a formal procedure to secure Akaev's resignation.
(RFE/RL's Kyrgyz Service contributed to this report.)
For more on events in Kyrgyzstan, see RFE/RL's dedicated website Revolution In Kyrgyzstan