The upper chamber also decided that the authority of the outgoing legislature would be prolonged until the election. The mandate of the legislature had been due to expire on 14 April.
Akaev was ousted two days ago following weeks of protests against what the opposition says were fraudulent parliamentary elections last month. Deputies from the parliament elected in that poll also met today in Bishkek.
Former opposition leaders now in power have suggested that a new parliamentary election would be held some time after the presidential poll.
Akaev has fled the country but says he has not resigned. His whereabouts remain unknown.
Bishkek residents yesterday witnessed new scenes of looting as plundering crowds rampaged through the city, targeting shops, supermarkets, and gas stations.
But the country's new authorities reacted swiftly and managed to regain control over the situation.
Police reinforcements were hastily dispatched to the city center, while law enforcement officers were given authorization to use their firearms.
Sporadic gunshots were heard throughout the night as a cold rain started pouring on the city.
Reports that several people were killed and up to 100 others wounded could not immediately confirmed.
Today, citizens were back on the streets and most cafes in central Bishkek reopened. Policemen backed up by Interior Ministry cadets started reappearing near official buildings.
"Most of those people who are now on the square have come from all the regions [of Kyrgyzstan]."
By mid-morning, dozens of protesters had progressively gathered on Alatoo Square in front of the historical museum, just a few meters away from the White House, as the headquarters of the government and presidential administration is known in Bishkek.
Khurmat Sydykov is a representative of the protesters who picketed the White House before rioters stormed the building on 23 March, forcing President Akaev to run away. He tells RFE/RL the people assembled on Alatoo Square have come from all areas of Kyrgyzstan.
"Most of those people who are now on the square have come from all the regions [of Kyrgyzstan]. They have nowhere to sleep, so they just gather here to spend the night," Sydykov said. Invalidated Results
Both chambers of the outgoing parliament, whose mandate has been restored after the Central Election Commission on 23 March invalidated the results of recent parliamentary elections, met today to assess the political situation after this week's upheaval.
In the meantime, members of the new, single chamber-parliament were meeting in another wing of the building.
Deputies failed to come to an agreement as to which of the two parliaments should be considered legitimate.
Talking to reporters after today's parliamentary session, upper chamber member Valeri Dil said he believed the question of who should be mandated to represent voters must be solved urgently:
"You saw the people on [Alatoo] square? You saw how yesterday they tried to storm the White House [for the second time]. They demand one thing -- that the results of the recent [legislative] elections be nullified. However, you understand that we live in a legal field. In my opinion, it would be wise now for the [old] parliament to set a date for presidential polls and then, within the next three months as envisaged by the constitution, to organize new parliamentary elections. That would help us get out of the present situation," Dil said.
The mandate of the old legislature officially expires on 14 April. Our correspondent says no agreement has yet been reached on what will happen after that date.
Photo Gallery: Bishkek, 24 March -- A Day In Pictures
U.S. Urges Opposition To Exercise Restraint, Follow Rule Of Law
Analysis: Will Opposition Leader Bakiev Be Kyrgyzstan's Next President?
Analysis: After The Dust SettlesFor more background on the crisis in Kyrgyzstan, see RFE/RL's dedicated website Revolution In Kyrgyzstan