Thousands were out in the streets of Kyrgyzstan's capital Bishkek on Friday as rival factions made grabs for power and embattled pro-Russian President Sooronbay Jeenbekov said he was ready to resign to end days of post-election chaos.

There has been little evidence of central government in Bishkek since a parliamentary vote in the ex-Soviet republic on Sunday sparked protests that morphed into violent unrest.

One person has been killed and more than a thousand injured in the violence, which has thrown the landlocked Central Asian nation into political turmoil.

On Friday Jeenbekov signed off on the resignation of the government in place before the election, which opposition parties say was rigged by massive vote-buying in favour of parties close to the president.

The election results were cancelled on Tuesday in a bid to bring calm, but that has done little to ease tensions.

Jeenbekov, who has not appeared in public since Monday, said in a statement on Friday that he was prepared to step down once a new government can be formed. "After legitimate executive authorities have been approved and we are back on the path of lawfulness, I am ready to leave the post of President of the Kyrgyz Republic," he said in the statement.

Supporters of various rival groups gathered in parts of the capital, each supporting its own faction or cause but none openly backing the current leader.

Several thousand people on Friday gathered in a square next to the building housing the prime minister's office to support a populist politician, an AFP journalist said.

Sadyr Japarov, a headstrong nationalist who was in jail before being released by allies during a night of chaos on Monday, is making a claim to be prime minister.

"(Japarov) will become prime minister and president and then everything will be all right," one speaker told the crowd, which was aggressive and threatened several journalists.

Russia as powerbroker 

Japarov was serving an 11.5-year sentence for hostage-taking prior to his release.

Across the city, followers of Kyrgyzstan's former president Almazbek Atambayev held their own rally where supporters held up placards demanding Jeenbekov leave the country.

Atambayev -- an ally turned foe of Jeenbekov -- was serving an 11-year sentence for his role in allowing a mob boss early release from jail during his presidency.

The former head of state was also freed by protesters during a night of tumult after results were announced.

A third rally organised by civic groups was underway in another part of Bishkek against organised crime, which many Kyrgyz complain is enmeshed with politics.

Russia is the dominant foreign power in Kyrgyzstan and has attempted to broker internecine disputes in the past. But it was unclear if even Moscow could help stabilise a fluid situation in the republic on Friday.

Stanislav Zas, the secretary general of the Collective Security Treaty Organization (CSTO), a Moscow-led security bloc, suggested that the bloc could play a "mediating role".

"We have that experience," said Zas.

One figure who seemed to have Moscow's trust is Omurbek Suvanaliyev, a former police boss who held talks this week with the head of Russia's FSB security service.

Suvanaliyev declared himself head of the State National Security Committee (GKNB) amid the chaos, but the agency said in a statement Friday that he had been "escorted" from its headquarters, noting the committee was not "a tool to achieve the selfish goals of certain groups".

Moscow said earlier this week it had beefed up security at a military base near the capital Bishkek.

If Jeenbekov were to resign, he would become the third leader from the former Soviet country to be felled by political unrest after uprisings unseated authoritarian presidents in 2005 and 2010.

He has ruled Kyrgyzstan, which shares a border with China, since 2017.