Wash the potatoes well and cook in boiling salted water for about 30 minutes. While potatoes cook, finely slice the green onion and place in a large bowl with the capers, olives, olive oil, and chopped fresh parsley. Add a few spoonfuls of the potato cooking water to the bowl.
Drain, peel, and slice the cooked potatoes while still warm. Add to the bowl and mix gently. Season with salt and pepper to taste.
Drain and flake the tuna, then add it into the potato mixture.