Bolivia – Imayra
Bosnia & Herzegovina – Kemal Monteno
Croatia – Karma
Czech Republic – Cechomor
Hungary – NOX
India – A.R. Rahman
Israel – Ofra Haza
Russia – Bi-2
Slovenia – Siddharta
Turkey – Tarkan
References :

*Jose Capmany (father and founder of Costa Rican Rock)
El Barco (The ship)
http://www.youtube.com/watch?v=MZvOxmA5zB4

*Gandhi
El Invisible (The Invisible)
http://www.youtube.com/watch?v=E6oiho9YJvY&feature=related

*Evolucion:
Ni vengo ni voy (Not coming neither leaving) the singer a jerk I know him personally he used to date one of my sisters a total arrogant a$$face but his band is cool
http://www.youtube.com/watch?v=-tmg1qIvnfo

* Suite Doble
Profanar ( desecrate)
http://www.youtube.com/watch?v=Qw4YsGFtQJk&feature=related
References :

I assume that you want countries that you have not already listed?

Andorra (Persefone) — Tech/Extreme Prog Metal
Armenia (Artsruni) — Prog Folk
Austria (Agnus Dei) — Prog Related
Bahrain (Osiris) — Neo-Prog
Bangladesh (Artcell) — Tech/Extreme Prog Metal
Belarus (Pesniary) — Prog Folk
Belgium (X-Legged Sally) — RIO/Avant-Prog
Bolivia (Climax) — Heavy Prog
Bosnia and Herzegovina (Emir Hot) — Progressive Metal
Bulgaria (Velislav Ivanov) — Neo-Prog
Chile (Abrete Gandul) — Eclectic Prog
Colombia (Hidden Path) — Progressive Metal
Costa Rica (Amarillo Cian Y Magenta) — Jazz Rock/Fusion
Croatia (Don’t Mess With Texas) — Post Rock/Math rock
Cuba (Anima Mundi) — Symphonic Prog
Czech Republic (Blue Effect) — Jazz Rock/Fusion
Ecuador (Ashler) — Progressive Metal
Estonia (B F) — Jazz Rock/Fusion
Georgia (Sinatlis Tselitsadi) — Eclectic Prog
Ghana (Osibisa) — Jazz Rock/Fusion
Guatemala (Alux Nahual) — Crossover Prog
Hungary (After Crying) — Symphonic Prog
India (Motherjane) — Heavy Prog
Indonesia (Abbhama) — Symphonic Prog
Iran (Arashk) — Progressive Metal
Israel (Ahvak) — RIO/Avant-Prog
Latvia (Holy Lamb) — Symphonic Prog
Lebanon (Rabih Abou-Khalil) — Prog Folk
Luxembourg (Le Grand Guignol) — Tech/Extreme Prog Metal
Macedonia (Vlatko Stefanovski) — Prog Folk
Malta (Different Strings) — Neo-Prog
Mexico (Agora) — Progressive Metal
Monaco (Edhels) — Neo-Prog
Multi-National (Aethenor) — Progressive Electronic
Pakistan (Mizraab) — Progressive Metal
Panama (Equinox) — Neo-Prog
Peru (Don Gato) — Jazz Rock/Fusion
Philippines (Fuseboxx) — Progressive Metal
Puerto Rico (Asi Somos) — Prog Folk
Romania (Accent) — Symphonic Prog
Russia (Actual Music Quartet Rsm) — Post Rock/Math rock
Serbia (Acid Rain) — Progressive Metal
Slovakia (Ako Doma) — Eclectic Prog
Slovenia (Katalena) — Prog Folk
South Africa (Robert Calvert) — Psychedelic/Space Rock
Switzerland (Agamemnon) — Psychedelic/Space Rock
Syria (Nu.Clear.Dawn) — Progressive Metal
Tunisia (Myrath) — Progressive Metal
Turkey (Altona) — Progressive Metal
Turkmenistan (Gunesh Ensemble) — Jazz Rock/Fusion
Uruguay (Drama) — Neo-Prog
Uzbekistan (X Religion) — Symphonic Prog
Venezuela (Vytas Brenner) — Eclectic Prog
Yugoslavia (Aerodrom) — Prog Related

I used a "select, distinct" from my personal database of bands –

So — there are bands listed "early" in the alphabet —

However, there are so many more — but, I wanted to get this done, before your question was "resolved."

I can pick-out the Best bands, at a later time, for you

Edit –

Yes — I have heard all of these bands, in one form, or another
References :

‘El Estuche’- http://www.youtube.com/watch?v=G8xbI2cZg-k
References :

India – Lata Mangeshkar
http://www.youtube.com/watch?v=IEmbhtywyMI

Czech Republic – The Ecstasy of Saint Theresa
http://www.youtube.com/watch?v=cL9-yj9kIpI

Belgium – Hooverphonic, Arsenal
http://www.youtube.com/watch?v=Tkn-SYf11lA
http://www.youtube.com/watch?v=ooWqGfqPlaE
References :