Kucera,16, stormed into the semifinals after beating Kenyan Ruinclife Baraka Ominde and 2-0 (6-0 6-2) in the quarterfinal on Thursday.
Meanwhile, Indian Rurik Rajini will take on Alexey Shibaev in another semifinal game on Friday.
Rajini advanced to the last four after seeing off Polish Olaf Wisniewski 7-5 6-2 in the quarterfinals while Shibaev made it to the same round beatingCanadian Jay Lin Gibson 6-3 6-4.
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Zosia advanced to the last four after overcoming Kenyan Cynthia Wanjala 6-3 6-2.
Rwanda won hosting rights for the ITF World Tennis Tour Grade 4 (J60) after successfully staging the ITF World Tennis Tour Grade 5 (J30) held in May.
The ITF World Tennis Tour Juniors gives players aged 18 and under the opportunity to travel the world and develop their talent in Tennis.
The first week of the competition in Kigali has attracted 44 boys from 16 countries and 25 girls from 14 countries from across the globe.
Rwanda records the highest representation in boys competition with 10 players while India (5) is the highest represented in girls category.