Karimov, 78, who has run Uzbekistan since it was a Soviet republic and wields sweeping powers, has no obvious successor.
Uzbek President Islam Karimov is in a stable condition in an intensive care ward after suffering a brain haemorrhage on Saturday, his daughter Lola Karimova-Tillyaeva wrote on her Instagram page on Monday.
Karimov, 78, who has run Uzbekistan since it was a Soviet republic and wields sweeping powers, has no obvious successor. This means that the eventual transition of power is likely to be decided within a close circle of his family and top officials.
"At the moment, it is too early to make any forecasts about his condition in the future," his daughter wrote. "I will be grateful to everyone who will support my father with prayers.
The government of Central Asia's most populous country said on Sunday that Karimov was undergoing hospital treatment, but provided no details.
A failure to reach consensus on a transition could destabilise the mostly Muslim nation of 32 million long targeted by Islamist militants and strategically located north of Afghanistan.
Karimov has no sons, who might have been regarded as heirs apparent in the patriarchal culture. His elder daugher, Gulnara, has not appeared in public since several media reported in 2014 that she had been placed under house arrest.
Karimov's second daughter, Lola, is Uzbekistan's ambassador to Paris-based UNESCO.