Uzbekistan seized Celil on March 27 acting on Interpol warrants issued by Kyrgyz and Chinese police.
Uzbekistan claims Celil, who was carrying a Canadian passport at the time of his arrest, is actually a Turkish citizen named Guler Dilaver.
Beijing believes he was involved in a May 2000 attack on a state delegation in China's western Xingjiang Province, the home region of Turkic-speaking Uyghurs.
Bishkek holds him responsible for the killing, in March 2000, of Nigmat Baizakov, the head of the Uyghur Society in Kyrgyzstan.
Protestors at the Bishkek rally, which was organized by a Uyghur rights group called Democracy, maintain that the charges brought against Celil are fabricated.