He was speaking to the press after meeting his Croatian counterpart Kolinda Grabar-Kitarovic.
Asselborn said he and Grabar-Kitarovic discussed Croatia's efforts in judicial reform, market competition, environmental protection, and other areas.
Grabar-Kitarovic said the talks addressed bilateral assistance, notably in legislative adjustment and the construction of administrative capacities.
Asselborn said Luxembourg had an obligation to help Croatia because of its experience.
Asked by the press why in all old EU member states, including Luxembourg, citizens strongly opposed enlargement to Southeast European countries, he said that was not correct.
Luxembourg has always advocated the position that Europe should enlarge to its east and southeast, Asselborn said.
The only alternative for Croatia is the road which guarantees dignified living and the stabilisation of Europe, and this is the EU, he said. That road is long but Luxembourg's government holds that this is the right path and I am convinced that Luxembourg's public feels the same way, he added.
Asselborn said both Luxembourg and Croatia had to invest a lot of effort in promoting the European notion, and added that his visit represented support for Croatia's efforts to promote this notion.
The minister said the EU was not only Strasbourg, Brussels or Luxembourg, but that Europe began in this region, with the political, economic and cultural cooperation of the countries in the region.
He recalled that Luxembourg had done the same after World War Two by cooperating with the Netherlands and Belgium, and often serving as arbiter in the settlement of French-Dutch issues.
Asselborn said he wished the same role and cooperation for Croatia, which he added represented a leader in the region as well as a bridge to Europe.
Grabar-Kitarovic thanked him on Luxembourg's support to Croatia since gaining independence and especially in the European integration process.
Asselborn said that during Luxembourg's EU presidency in the first half of 2005, the most energy had been invested in the issue of opening negotiations with Croatia.
I was very happy on 3 October 2005, when we found a positive solution for Croatia and for the EU, he said.
Today's talks also addressed bilateral trade, which is modest, said Grabar-Kitarovic, adding that in 2004 Croatia's exports to Luxembourg were USD602,000 while imports were 11 million.
Asselborn said Croatia was a favourite destination among Luxembourg's tourists.
Grabar-Kitarovic underlined Luxembourg's significant assistance in mine clearance, with EUR605,000 invested in six projects so far, notably in the demining of farmland.
Asselborn is also scheduled to meet Croatian President Stjepan Mesic and Prime Minister Ivo Sanader.