Brussels wants Slovenia, Croatia to resolve border row this week
The border row involves a small piece of land and sea and dates back to 1991.
"It is really the moment of truth now and we should all try to settle this before the European council summit meeting on Thursday," Rehn said as he entered EU foreign ministers talks in Luxembourg.
The foreign ministers were to hold talks with their Croatian and Slovenian counterparts on the sidelines of the talks.
"I certainly hope that we could complete and conclude the process," said Rehn.
The EU commissioner was first to hold talks on the matter with the "trio" of past, present and future holders of the European Union presidency: France, the Czech Republic and Sweden.
"I understand the trio and Rehn have some new ideas, even a new proposal today, and we are looking forward to this new proposal," said Slovenian Foreign Minister Samuel Zbogar as he arrived for the talks.
The border row involves a small piece of land and sea and dates back to 1991, when both countries proclaimed independence from the former Yugoslavia.
Slovenia joined the EU in 2004. Croatia hopes to become the EU's 28th member by 2011.
A key point for Ljubljana is securing free access to international shipping waters by getting a corridor that would cross Piran bay which is currently controlled by Zagreb.
The 18-year-old border dispute has blocked Croatia's EU membership talks since December, with Slovenia demanding it be resolved before the accession negotiations resume.
Finnish Foreign Minister Alexander Stubb voiced qualified confidence as he entered the Luxembourg talks.
"I am sure we will find a solution at the end of the day, not necessarily today," he told reporters, while EU foreign policy chief Javier Solana said he thought an agreement was close.
In April Rehn proposed setting up a tribunal to arbitrate in the dispute.
However, while Slovenia views EU mediation as a way to resolve the dispute, Croatia considers it simply a stepping stone to a resolution before the International Court of Justice in The Hague.
According to one diplomat, Slovenia could become more flexible on the issue now that European elections are over.
EU member states, especially Sweden, France and Germany want "to put more pressure on Slovenia" to accept a compromise, another diplomat said.
Despite Slovenia's current veto, the European Commission still hopes to finish the technical negotiations on Croatia's EU membership bid before the end of the year.