Translation:Our countries have fought twice.
It's quite possible to say "Our countries fought each other twice." But in the same way we would ordinarily understand the sentence "Two people fought" to mean that they fought each other, it is not generally necessary to say 'each other.' However, in some contexts this may not be clear. If we asked, "Did your countries fight in any (world) wars?" the answer "Yes, they fought" could simply mean they participated on either side, not necessarily against each other.
It is quite usual in English to omit the "each other" implied by "sobě", however I expected the "each other" to be the main translation with it omitted as an acceptable alternative rather than the other way round. It leaves no room for misunderstanding as to who fought who(m).