The 62-year-old Atambayev, who served as president of the Central Asian country from 2011 to 2017, has been accused by his successor and former ally, Sooronbai Jeenbekov, of a range of crimes, including corruption and illegal land purchases.
He urged his supporters to rally Thursday in the capital, Bishkek, to demand Jeenbekov's resignation.
Around a thousand police and special forces officers were taking part, while the same number of supporters of Atambayev were defending the residence, she said.
Apart from the serviceman who died of his wounds, the Health Ministry said 35 other people were wounded in the clash, including 15 police officers.
The violence has raised the threat of fresh turmoil in the former Soviet country, which borders China and hosts a Russian military airbase.
"About 200 police officers again started storming the residence, they are using stun grenades".
Kyrgyz former President Almazbek Atambayev, who was stripped of legal immunity after a parliamentary vote, and his supporters attend a meeting with journalists in the village of Koy-Tash near Bishkek, Kyrgyzstan June 27, 2019.
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Police were seen firing tear gas into crowds that had gathered outside the heavily fortified compound as they looked for a way to enter it.
He is now being held at the building of the State National Security Service (GKNB) while hundreds of his supporters gathered in central Bishkek and blocked a major thoroughfare. The GKNB stated that the soldiers were equipped "only with rubber bullets", while Atambayev's supporters had lethal ammunition.
"Jeenbekov must now decide whether to escalate violent confrontation with Atambayev's supporters or negotiate", Marat said. Atambayev has said that he also fired several shots when police came to arrest him Wednesday, adding that he "tried not to hit people".
But Medvedev said he would discuss the matter in his meetings with the Kyrgyz leadership, Russia's TASS news agency quoted him as saying on Thursday.
MOSCOW-Gunfire was heard outside the residence of the former president of Kyrgyzstan as police moved in to try to arrest him.
Russia's foreign intelligence chief Sergei Naryshkin warned that the tensions have reached a "dangerous scale" and Foreign Ministry spokeswoman Maria Zakharova urged the conflicting parties to show 'responsibility and common sense'.
At the time the two men were close allies but relations later soured, and observers say Mr Jeenbekov moved to sideline his predecessor politically past year. "Kyrgyzstan has already exhausted a limit for revolutions in this century".