In an open and friendly atmosphere Mesic and Asselborn agreed that relations between Croatia and Luxembourg were good, the statement said.
Asselborn said it was necessary to continue developing economic relations and added that Luxembourg was the seventh biggest investor in Croatia.
Luxembourg will continue supporting Croatia on its path to the EU, he said, pointing to the importance of continuing reforms in the judiciary, agriculture and environmental protection and the importance of cooperation with neighbouring countries.
Mesic thanked Luxembourg for its support to the de-mining process in Croatia and the process of its integration with the EU, stressing the need to establish closer economic ties.
Speaking of cooperation with neighbouring countries, Mesic said that the crucial issue was the individualisation of guilt, a process in which the Hague war crimes tribunal was providing assistance.
Asselborn also met the chairman of the parliamentary committee on foreign policy, Gordan Jandrokovic, the parliament's public relations office said.
Jandrokovic thanked Luxembourg for its support to Croatia's efforts to start EU entry talks, which he said was above the usual support provided by one country to another, and for its trust in the sincerity of Croatia's policy.
Asselborn said he was confident of Croatia's potential and the fact that it was a law-based country. He inquired about the parliament's role in EU entry talks and its position on reforms as well as the existence of political will to implement them.
Croatia is fully aware of responsibilities arising from its future EU membership, Jandrokovic said, adding that there was a consensus of all relevant political forces and parties in the country regarding that foreign policy priority.
Jandrokovic said there were three key tasks that were being performed simultaneously - the implementation of reforms, EU entry talks and provision of information on the EU to the public.
Asselborn also inquired about the parliament's position on the European Commission's proposal for the establishment of a free trade zone in the Western Balkans.
Jandrokovic said that the public in Croatia was distrustful towards the proposal considering the country's recent history and the aggression it was exposed to and that it feared that stronger regional ties would make Croatia a hostage to the Western Balkans.
Nevertheless, Croatia is willing to be a bridge between EU countries and Southeastern Europe, and even serve as a model, but it wants clear prospects of EU membership and an individual approach, Jandrokovic said.
Building ties within the Central European Free Trade Agreement can help Croatia play an important role in regional integration, Jandrokovic added.