Vondra was one of participants of the EU Troika meeting in Brussels on Wednesday evening convened by Rehn in a bid to resolve the said bilateral row.
Also attending were Swedish Foreign Minister Carl Bildt and French Ambassador Pierre Selal.
The Troika consists of France, the Czech Republic and Sweden - the former, present and future EU chairs.
The exchange of opinions (at the meeting) was good. I think that our joint position is to support Commissioner Rehn's efforts and we expect some results at the intergovernmental conference, Vondra said.
Rehn also said that he had received the backing from the Troika for his initiative.
The discussion was useful. We have agreed that the Czech Deputy Prime Minister will speak on behalf of the EU. The Troika supports the Commission's initiative and encourages the two countries to make constructive engagement so that we can achieve results before the intergovernmental conference in late April, Rehn said.
Minister Bildt and Ambassador Selal were not available for comments.
Earlier in the day, Rehn's meeting with Croatian Foreign Minister Gordan Jandrokovic and Slovene Foreign Minister Samuel Zbogar, was postponed because the European Commission has not yet received Croatia's response to Rehn's latest compromise solution concerning the Croatian-Slovene border dispute, the Commission reported.
Instead, Rehn held the meeting with the European Union Troika on Wednesday evening.
Minister Jandrokovic will present Croatia's proposal for the settlement of the Croatian-Slovene border dispute and the lifting of Slovenia's blockade of its EU membership talks at the first opportunity, since the meeting with EU Enlargement Commissioner Olli Rehn and Slovene Foreign Minister Samuel Zbogar, scheduled for Wednesday, has been postponed, the Croatian foreign ministry said in a statement on Wednesday afternoon.
"As he was travelling to Brussels (from The Hague, where he attended an international conference on Afghanistan), Minister Gordan Jandrokovic received information about the postponement of the meeting which was to have been organised today by EU Enlargement Commissioner Olli Rehn," the statement said.
At the meeting, Jandrokovic was to have presented Croatia's proposal for the settlement of the Croatian-Slovene border dispute and the issue of Slovenia's blockade of Croatia's EU entry talks.
"Since the meeting has been postponed, Minister Jandrokovic will present Croatia's proposal at the first opportunity," the statement said.
Asked why Croatia had not responded to Rehn's latest initiative, Vondra said this evening that they were waiting for it.