BISHKEK, March 28 (AFP) - The new leaders of Kyrgyzstan, brought to power by a lightning revolution in the Central Asian state, met with the head of Europe's leading security organisation on Sunday as they struggled to end a parliamentary split that threatened a fragile return to calm.

The general secretary of the Organisation for Security and Cooperation in Europe (OSCE), Jan Kubis, held talks with Kurmanbek Bakiyev, whom parliament named acting president ahead of new presidential elections set for June 26, along with other interim officials.

The 15-year Soviet-era regime of Askar Akayev was toppled last Thursday amid chaotic opposition demonstrations protesting the results of a March 13 parliamentary runoff vote seen as fraudulent by much of the population, the OSCE and other observers.

Akayev, a 60-year-old former physicist credited with bringing economic reform and democracy to his country after the collapse of the Soviet Union but who became increasingly autocratic in recent years, has not been seen since his ouster, which he condemned and refused to recognize in a statement on the Internet.

Several opposition figures such as Bakiyev have been tapped to fill the power void pending the new presidential elections.

They eventually brought an end to looting and street violence that raged for two days, but jockeying in the parliament has broken out between the old legislature and the new one chosen in the March poll.

With Kubis at his side, Alojz Peterle, the OSCE representative in Central Asia, urged Kyrgyzstan's power brokers to resolve their differences peacefully.

"The OSCE wishes that the parties involved are able to use political dialogue in order to get a conclusion for the benefit of all the country," Peterle told reporters in Bishkek.

"Now is not the time for discussing different reasons for developments that occurred, but how to deal with the consequences of those developments," Peterle said.

Kubis did not speak at the news conference.

An OSCE official, Marina Dmitrieva, told Russia's Moscow Echo radio station that the organization considers "holding a presidential election next June too ambitious an intent on the part of the new authorities."

In Bishkek, shattered glass has been swept up from the sidewalks, broken windows have been replaced and kiosks trading foreign currency began reopening, signaling a return to normalcy after days of unrest.

But as vendors again set out their wares, an intense debate raged inside parliament as rival lawmakers laid claim to being the legitimate representative of Kyrgyzstan's five million people.

The opposition has claimed that Akayev's administration falsified the parliamentary elections in order to stack the chamber with his supporters, and some deputies refuse to cede to the new chamber sworn in the day before Akayev's regime crumbled.

On Sunday, the new deputies appeared to be gaining an upper hand, after the central election commission, the country's new security chief and prosecutor general backed the new chamber during a joint session of the rival chambers.

"You had been elected for five years and your mandate has expired," Felix Kulov, an opposition leader under Akayev who was released from prison following the protests and appointed the nation's security chief, told deputies.

"According to the law, the new parliament has to start work," Kulov said. "There are people whom I don't like in the newly elected parliament, but I am a law-abiding citizen and will obey the new parliament."

Kulov told the deputies that during Akayev's regime he had lost an election because of interference of the authorities.

"But despite this, I acknowledged my defeat," he said. "We're not hicks here, we're members of the UN."

Deputies from the old parliament fear that the newly elected deputies could annul the new presidential elections and maybe even stage a counterrevolution.

Deputies failed to come to an agreement by the end of session early Sunday afternoon.

Bakiyev said late Sunday that he was prepared to ensure Akayev's security, should the ousted leader return to Kyrgyzstan. "I will try to ensure conditions for his security," Bakiyev was quoted as saying by the RIA Novosti news agency.