Austrian Chancellor Wolfgang Schuessel has said it will be "hard and difficult" to revive the draft EU constitution, but not impossible.
Chancellor Schuessel said the EU needed to prove its worth to citizens
Austria has been tasked with reviving debate on the EU's future after the rejection of the constitution by French and Dutch voters last year.
It will report back to an EU summit in June, with ideas about what to do next.
"I think we can at the end of the Austrian presidency present some success," Mr Schuessel said.
He was speaking as the Austrian government and the entire 25-member European Commission held talks in Vienna to discuss plans for the next six months.
Mr Schuessel said on Sunday there should be a "dialogue with the people" in all European nations "about the border of Europe, about the institutions, about where we are going and not just about where we are coming from."
The constitution has been on ice since it was rejected by the French and Dutch voters last May and June, and was all but declared dead by the British government.
"What is the role of Europe, what is the delivery of Europe, what is the benefit for the everyday citizen?... We are going to have to work on this very intensively," Mr Schuessel said on Monday.
"And as long as we can't answer in a correct and fair way these real questions, then the constitution is hard and difficult to revive."
He added that special efforts would have to be focused on France and the Netherlands.
Foreign Minister Ursula Plassnik said she would visit Paris and The Hague this week.
Austria is the most Eurosceptic country in the EU, and many there will resist thawing out the constitution, says the BBC's Europe editor Mark Mardell.
Austria's right-wing Vice-Chancellor Hubert Gorbach said on Sunday that it was damaged beyond repair and could not be "doctored" and put forward again for ratification.
"We need to go back to the start, we need to newly regulate the powers... We need less regulation from Brussels and more powers to the Europe of the regions," Mr Gorbach said.
Finance Minister Karl-Heinz Grasser said the Austrian presidency should focus not on resurrecting the constitution but on fighting unemployment.