The event was organised by the Croatian Emigrants Association and is held under Mesic's auspices.
Mesic congratulated minority representatives on centuries of efforts invested in preserving the Croatian language and culture.
He said Europe's history was full of abuse of minorities, but added indigenous Croatian minorities had been loyal to the countries they lived in, thanking them for it.
Mesic went on to say that the destiny of minorities would depend on local elections in neighbouring countries, adding that Croatia would stand behind its minorities.
"Europe is being built on new foundations and no one will constitute a majority, which is the realisation of your ancestors' dreams of coexistence," Mesic said, adding that "in this Europe, you are becoming genuine bridges of cooperation for the first time".
Also in attendance was Croatia's European Integration Minister Kolinda Grabar-Kitarovic and numerous senior officials and diplomatic representatives of countries from which the participants in Croatian Minorities Week have arrived.
Until September 25, indigenous Croats from a dozen European countries will present their culture, problems, and prospects.
Organisers said this year's event would feature for the first time Croats from Slovenia and Macedonia.
According to estimates, about 300,000 Croats whose ancestors left their homeland due to long wars now live in Austria, the Czech Republic, Italy, Hungary, Macedonia, Romania, Slovakia, Slovenia, and Serbia and Montenegro.