Moeller, who was on a working visit to Zagreb, met Grabar-Kitarovic to discuss the progress of Croatia's negotiations with the EU and prospects of the bloc's further enlargement.
Asked by a reporter to comment on the statement by EU Enlargement Commissioner Olli Rehn that Croatia would not become a member before the end of the decade, Grabar-Kitarovic said that in all his meetings Rehn had expressed his optimism about Croatia joining the EU as soon as possible.
"Although no one has promised Croatia when it will enter, because that is not possible at the moment, (...) we will continue our efforts to speed up the talks and ensure that this happens as soon as possible," she added.
Asked if the enlargement process should be halted until the adoption of the common constitution, Moeller replied that Denmark had made certain promises and would stick to them.
We are also talking about enlargement fatigue of some sort, but we keep our promises, he added.
The two ministers also discussed security in Southeast Europe. Moeller was interested in the further development of stability and security in the region since Denmark was the current president of the UN Security Council.
Also discussed were issues relating to global security and cooperation in combating terrorism and other security threats such as trafficking in arms, people and drugs.
On the subject of bilateral relations, which were described as traditionally very good, Moeller and Grabar-Kitarovic agreed that it was necessary to intensify dialogue both on bilateral relations and on the European future and international security.
Noting that Denmark had invested 67.7 million euros in Croatia since 1993, Grabar-Kitarovic expressed hope that Croatia would attract more and more investments from Denmark, particularly greenfield investments.
Moeller concurred, saying that Denmark wanted to see more Danish companies coming to Croatia to invest.
Grabar-Kitarovic thanked Denmark for its support in the pre-accession period, adding that Denmark would provide Croatia with about 1.8 million euros in aid as part of a bilateral programme aimed at assisting in building public administration in the 2005-2007 period.
The Danish minister also met Prime Minister Ivo Sanader on Wednesday and was scheduled to meet President Stjepan Mesic on Thursday.