Mesic described the meeting as "cordial, open and constructive" and the cooperation between the two countries as "increasingly better".
Mesic began a two-day official visit to Austria on Monday, during which he was also scheduled to meet Chancellor Alfred Gusenbauer and Parliament Speaker Barbara Prammer.
Mesic and Fischer first met privately, after which they were joined by their respective delegations. The talks focused on bilateral cooperation and multilateral issues, including relations between Croatia and Slovenia and the situation in Kosovo.
As regards the cooperation between Austria and Croatia, the two presidents also highlighted and praised good cooperation between the Croatian and Austrian judicial authorities in the case of former Croatian assistant defence minister Vladimir Zagorec, who is suspected of embezzling funds intended for Croatia's defence during the 1991-1995 war of independence.
"That sensitive case is an example of good cooperation between the judicial authorities," Fischer said.
Mesic said that in the case of General Zagorec Croatia was trying to track down misappropriated defence funds.
"Hundreds of millions of euros changed their owners and then we found out that there were about a hundred bank accounts. Now we have to establish where the money is," Mesic said.
The Croatian president informed his host about several outstanding issues between Croatia and Slovenia, including the border issue and the Ljubljanska Banka issue. "We want nothing else but equal treatment for all the depositors of the bank," Mesic said.
On the subject of the border dispute, Mesic said that both Croatia and Slovenia should accept a solution proposed by an international judicial body, such as the International Court of Justice in The Hague, adding that Croatia was ready to "accept in advance any court decision."
Croatian-Slovene relations are "a bilateral problem between Croatia and Slovenia in which Austria will not interfere," Fischer said.
Fischer said he was pleased with the progress of Croatia's membership negotiations with the European Union as well as with the economic cooperation between Austria and Croatia.
"Our bilateral relations are excellent," Fischer said, adding that he was confident that next year trade between the two countries would "break the sound barrier of two billion euros."
Stressing that Austria was the leading investor in Croatia today, Mesic thanked Austria for its assistance during and after the war, particularly in the reconstruction of the eastern town of Vukovar and the central region of Lika and in the economic revival of the Slavonia region.
The two presidents also discussed developments in Serbia's breakaway province of Kosovo, stressing that they supported the plan proposed by UN mediator Martti Ahtisaari and expected a peaceful resolution of the Kosovo crisis.