Akbarali Abdullaev – a nephew of Karimov's widow, Tatyana Karimova – stated at the hearing on February 23 that he would face "death" if extradited to Uzbekistan, RFE/RL wrote.
However, the judge ruled that he must remain in custody for one year while a decision on his possible extradition is under consideration.
Read alsoFirtash released on EUR 125 mln bail on Friday – mediaAbdullaev, 33, was detained at Kyiv's Zhulyany International Airport in January where he arrived with Uzbek and Dominican passports.
He was later sent to one-month pretrial detention, which expired on February 22.
Abdullaev was charged in Tashkent with embezzlement and financial fraud in 2014.
It is not clear how or when he left Uzbekistan.