During the talks, Mesic said that Croatia had good bilateral relations with Finland, the country that takes over the EU presidency on 1 July, and stressed the need for the two countries to enhance economic ties.
According to a statement issued by the President's Office, Vanhanen said that EU enlargement was a successful process and that it was new EU members and countries yet to be admitted to the bloc that were witnessing the fastest economic growth.
All countries in the region must have a European perspective regardless of the duration of the accession process, the Finnish prime minister said.
Speaking of Croatia's aspirations to join the EU, Mesic said that investment in the country was also in the interests of the EU because it meant investing in its own market and future.
The two officials also discussed the continuation of cooperation in the defence sector.
The Finnish guest was also received by the Speaker of the Croatian Parliament, Vladimir Seks, with whom he discussed Croatia's progress towards the EU and Finland's experience from pre-accession talks.
Vanhanen invited Seks to attend a parliamentary ceremony in Helsinki on 1 June on the occasion of the 100th anniversary of the Finnish Parliament.