She told the press these countries called for a decision on the date as soon as possible and that at the same time Croatia had to prove that it was fully cooperating with the Hague war crimes tribunal.
Plassnik was attending a meeting of the European Union foreign ministers.
She said some EU countries clearly indicated that a positive decision on Croatia was expected soon.
The chairman of the Council of the European Union, British Foreign Minister Jack Straw, briefed the meeting on the latest conclusions of the EU task force evaluating Croatia's cooperation with the Hague tribunal.
According to the task force, Croatia has made headway in the implementation of its action plan to close the issue of Ante Gotovina, the fugitive general wanted by the Hague war crimes tribunal, but this progress is not sufficient to warrant the assessment that cooperation with the UN court is full, which is the condition for launching accession negotiations.
"I'm sorry there has been no headway regarding Croatia today. We will address this again in September at an informal meeting of foreign ministers and I hope that this will be a beautiful autumn for Croatia," Slovene Foreign Minister Dimitrij Rupel told the press.
Before today's meeting, Straw said the EU task force for Croatia would meet in September and that a new assessment by chief prosecutor Carla del Ponte was expected in late August or early September.
"We all have concluded that the time is coming when the decision on launching the negotiations has to be made. We all have supported Croatia and the need for the EU to expand to the western Balkans, because that will mean stability and prosperity for the region," said Rupel.