Drnovsek, who initiated the "informal meeting between friendly neighbours," said earlier this week not much should be expected from it and that it would be an opportunity to share views on European and bilateral issues.
"Slovenia is interested in our neighbour Croatia starting EU membership negotiations as soon as possible and in setting a date for them as soon as possible," said Drnovsek.
Despite several outstanding bilateral issues which occasionally strained relations, Ljubljana has in recent weeks resolutely lobbied for opening the Croatia-EU entry negotiations, which Brussels postponed due to Zagreb's failure to hand over fugitive general Ante Gotovina to the Hague war crimes tribunal.
"Slovenia needs Croatia and Croatia needs Slovenia, and this goes for all areas, mostly for the economy," Drnovsek said today.
On Tuesday he said on Slovene Radio that Ljubljana's support to Zagreb was an attempt to create a climate in which it would be easier to close outstanding issues -- the demarcation of the state border, the settlement of a former Slovene bank's debt to Croatian depositors, and the jointly owned nuclear power plant Krsko.
Drnovsek said the political climate had changed and that it was again time to consider bilateral issues in a rational and unburdened fashion.
He added that if that did not work out there was always arbitration.
A long-standing issue has been the delimitation of the border, notably on the sea. A border deal was reached in 2001 by Drnovsek in his capacity as prime minister and his then Croatian counterpart Ivica Racan. Croatia subsequently abandoned the deal, but Slovenia continues to consider it good and valid.
Mesic told the same press conference the Drnovsek-Racan deal constituted an attempt to close outstanding issues as soon as possible.
"The intention was to intensify cooperation," but the public on neither side was ready for it at the time, said Mesic.
The two presidents also discussed a tentative Slovenia-Italy-Croatia meeting on the common past.