Now 39, the former Roma striker signed for the Viola after coming off contract at Fenerbahce.
He told San Marino TV: "Yes, yes, I'm enjoying it. It showed today too, right? Especially with all these fans of ours who came today. It's my first time in San Marino and it went well.
"I don't set myself any limits. Also because when you reach a certain age—next year I'll be 40—I'm definitely not young anymore. But I still feel good in the national team and also with Fiorentina, and I continue to give my all there, as I do here for the national team.
"Because with the national team, it's a different thing; you play with more heart. And then when I see all these fans of ours who came today, I'm truly proud to still be able to play and give my all for my country. And obviously, I'll continue as long as the coach tells me I'm needed."
On Fiorentina's hopes this season, Dzeko also said: "We're hoping for a good one. We started with two away draws. It's true that winning is never easy. We saw in the first two matchdays that the championship is increasingly difficult and there are no easy games.
"Now we play Napoli at home, against the Italian champions. They are definitely the favorites for the Scudetto. But the team is there, obviously. New coach, lots of new players. Maybe we still need a little time to get to know each other better. But we hope the more time passes, the better we get."