The group identifies the defendants as being Azat Pulatov (aged 55), Mirsabit Miryusupov (51), and Yori Baltiev (70).
All three are Tashkent residents and were arrested in February. They are also accused of plotting against Uzbekistan's constitutional order and national security.
The rights group says their trial adjourned and will resume on August 15.
On August 3, a Tashkent court sentenced 14 alleged Hizb ut-Tahrir members to between seven and 12 years in jail.
Rights campaigners have criticized Uzbek President Islam Karimov for cracking down on all forms of political and religious dissent through unfair trials.
Arms and leaflets allegedly confiscated from Hizb ut-Tahrir members in Kyrgyzstan in May (RFE/RL)
ATTRACTIVE TO THE YOUNG: It is virtually impossible to estimate the size or composition of Hizb ut-Tahrir's membership in Central Asia, because the controversial movement is banned in most places. But some observers say anecdotal evidence suggests the group's core of younger members is growing....(more)