Lajolo also expressed satisfaction with the implementation of treaties signed between the Vatican and Croatia in 1996 and 1998.
He arrived in Croatia over the weekend at the invitation of the Croatian Foreign Minister to attend a ceremony marking Croatian Diplomacy Day, which is celebrated on 7 June, in memory of the move by Pope John VIII who on that day in the 9th century recognised Prince Branimir as the ruler of Croatia.
Lajolo told the press that the Vatican had always advocated Croatia's full membership in the European Union and that Croatia's society could be perceived only as a European society.
He added that the Vatican was not an EU member but that it could freely express its position, and that the Catholic Church was present in every EU member-state.
Croatia's Grabar-Kitarovic told reporters that "relations between Croatia and the Vatican are excellent and are constantly being enhanced".
"We are grateful to the Holy See for the support it has offered since our country gained independence. We are glad to see that Pope Benedict XVI is pursuing the same policy as Pope John Paul II whom we regard as our advocate," the minister said.
Asked by reporters to assess the implementation of treaties between Croatia and the Holy See, Lajolo said "the Church may have some objections to the pace of implementation but there are objective problems and we do not complain. We are satisfied with the implementation of the agreements".
In 1996, Zagreb and the Vatican signed treaties regulating legal relations, the Military Diocese and relations between the schooling system and the Church. Two years later they signed treaties on economic relations including restitution of the church property.
On that occasion, the then State Secretary Angelo Sodano said that the agreements with Croatia would serve as models for similar treaties which the Holy See intended to sign with other countries in transition.
Currently, some members of the Catholic Church as well as other churches seem to be dissatisfied with the pace of the process of restitution. In addition, there is a grudging acceptance in those circles of the fact that pecuniary compensation is preferred to the return of real estate to previous owners.
Lajolo expressed satisfaction with the fact that Croatia and the Vatican shared the same position on the promotion of cooperation between countries in southeastern Europe, particularly in the area of the former Yugoslavia.
Later in the day, Lajolo was received by President Stjepan Mesic.
During the meeting with Mesic, he said that the Holy See treated Croatia as a natural part of the EU and firmly believed that Zagreb would easily meet the membership criteria.
After the talks, Lajolo described relations between Croatia and the Vatican as harmonious and friendly, adding that this was evidenced by an agreement on the restitution of church property signed in Zagreb today.
"The Holy See is in favour of the possibility of setting up a Catholic university in Zagreb," the Vatican official said adding that this could be a great contribution of the state and the Church to the Croatian society.
Lajolo also held talks with Prime Minister Ivo Sanader.
Earlier in the day, Sanader and the primate of the Catholic Church in Croatia, Cardinal Josip Bozanic, signed the agreement regulating the right of the Zagreb Archdiocese to become owner and use the "Kralj Tomislav" military barracks for its purposes.
The military complex, given to the Catholic Church as compensation for some other buildings in Zagreb owned by the Church until nationalisation in 1945, is to be used for the establishment of a Catholic university.
Bozanic said that the church property served for the common weal, for religious services, culture and charitable activities.