This was the second informal presidential meeting of the three countries. The first meeting was held in Vienna in March 2014, involving Fischer, Pahor and the then President of Croatia, Ivo Josipovic.
Pahor, who was the host of today's meeting, Grabar-Kitarovic and Fischer agreed that their next meeting would take place in Alpbach during a forum in that western Austrian town in August.
Addressing a news conference after their talks, Croatia's Grabar-Kitarovic described such trilateral meetings as a useful format of meetings of the countries that shared the same values.
The three presidents advocated the enlargement of the European Union.
"Enlargement has empowered the European Union, and this process should continue," the Croatian president added.
She explained that Croatia supported the EU prospects of its neighbours, notably of Bosnia and Herzegovina, provided that they met all the criteria and implement the necessary reforms.
As for open issues between Croatia and those EU aspirants in the region, Croatia does not want to impose ultimatums but expects them to make strong efforts to solve the remaining outstanding issues, Grabar-Kitarovic said, noting that a settlement of those issues seemed to be at a stalemate in recent years.
Slovenia's Pahor said he was satisfied to see that his second meeting with Grabar-Kitarovic affirmed the friendly bilateral relations.
He said that other EU aspirants in the region should learn the lessons from the Slovenia-Croatia relations while the latter had been on its journey towards the EU, adding that the sooner the issues were settled, the better.
Austria's Fischer said that the European Union proved to be a "visionary project" that had brought many years of peace and stability to Europe, which was why it should be further developed.
Fischer said that his country supported the admission of all southeastern European countries to the EU, and he particularly advocated the admission of Macedonia, provided that it assured EU members that it deserved that.
I want the EU policy to strictly abide by its principles, borders can be changed only peacefully and Russia failed to respect this, Fischer said, adding that although he appreciated the contribution of Russia to the victory in the Second World War, he would not attend this year's Moscow Victory Day Parade.
The Austrian president also called for a prudent and forward-looking path when it comes to the Ukraine crisis and the relations with Russia, but he admitted that the problem did not lie only in the Ukraine crisis but also in security erosion on the south and in the Mediterranean basin.
Grabar-Kitarovic said that 70 years after the end of WW2 and 20 years after Srebrenica, Europe was faced with security threats such as the Ukraine crisis and this issue should be settled politically in parallel to the preservation of Ukrainian sovereignty.
She commented that a certain crisis of values in Europe and "erosion towards" the European project were under way.
Grabar-Kitarovic announced that Croatia would organise a conference in October on transport policies and energy, having in mind efforts to seek alternative sources and distribution routes for energy.