Bush flew into Croatia on Friday, arriving from the Nato summit in Bucharest, the Romanian capital, where Croatia and Albania were formally invited to join the alliance.
Croatia and Albania become the 27th and 28th members of Nato once the accession and ratification process has been finalised, which alliance officials hope can be accomplished within a year.
Speaking on Friday, Bush paid tribute to Croatia's contribution of some 200 troops to the Nato force in Afghanistan.
"I appreciate friends who stare evil in the face and understand there's a better tomorrow," he said.
"We are honoured to be your trusted ally."
Bush and Stjepan Mesic, the Croatian president, discussed issues in the region, including Serbia and Kosovo, as well as energy matters and terrorism, Carlton Carroll, a White House spokesman, said.
In a toast to Bush at dinner, Mesic, a vocal opponent of the US-led invasion of Iraq, also praised the two countries' relations.
Croatia's government sees Bush's two-day visit as a sign that the country is now embraced by the West, a change from the early 1990s when Washington and other Western powers were distrustful of the Balkan states.
But ties were strengthened when the US aided Croatia in the final phase of its 1991-95 war for independence from Serb-dominated Yugoslavia.
There are still points of contention in the relationship, including Croatia's refusal to agree immunity for any US citizens sought by the International Criminal Court.
Bush will continue on to Russia's Black Sea resort of Sochi later on Saturday.
There he will try to ease tensions with Vladimir Putin, the Russian president, over missile defence and Nato expansion, before the Putin's term ends in May.
At the Nato conference in Bucharest Putin called on alliance leaders for better relations, saying: "Let's be friends, guys."