Islamic Jihad Movement in Palestine was created in 197#.

The Palestinian Islamic Jihad (PIJ)

Egyptian Islamic Jihad is a violent Islamist organization which wishes to make Egypt a state governed by a repressive version of Islamic Law (like ISIL is currently doing) and would wish to use the Egyptian Armed Forces to conquer Israel and "liberate" Palestine.

a jihad

There are over 50 Islamic countries, so Palestine is certainly not the only Islamic country, but if you are considering Israel and Palestine, yes, Palestine is the Islamic country while Israel is the Jewish country.