The European Parliament is debating a motion expressing concern at the political impasse in Northern Ireland.
Talks involving the British and Irish governments and the five executive parties are continuing at Stormont.
Mr Robinson said he had been stressing in Brussels that they "genuinely and sincerely want to get a satisfactory outcome to the talks process".
"We are going to put everything we have into getting that outcome," the DUP leader said.
"Until you come out with agreements at the end of a process, there's always scepticism and I think that's something you have to take for granted.
"It gives us the encouragement to try and prove the sceptics wrong."
Speaking in Brussels ahead of Wednesday's debate, he said: "In the early parts of any talks process, people keep their cards close to their chest - they state their positions, and it's really at the latter end of it that you test the other people who are around the table to see how far they are prepared to go on various issues."
The motion being debated by MEPs has been endorsed by a cross-section of parliamentary groups, and has been signed by Sinn FÃ©in's Martina Anderson and the UUP's Jim Nicholson.
It expresses concern that the implementation of the peace process has reached an impasse, and urges all parties "to work constructively towards a lasting resolution of the conflict and the full implementation of the Good Friday Agreement and subsequent agreements for a long-lasting and enduring peace".
It says continuing violence by "fringe elements" is undermining the peace process, and "stresses the need to combat such criminal activity by tackling existing economic challenges such as unemployment and low incomes and living standards".
The motion also says the European Parliament stands ready to offer any assistance it can to political parties in Northern Ireland.
It invites Northern Ireland's first and deputy first ministers to address the European Parliament "upon the successful completion of the all-party talks".
Both Mr Robinson and Ulster Unionist leader Mike Nesbitt have been in Brussels this week ahead of Wednesday's debate.
Deputy First Minister Martin McGuinness of Sinn FÃ©in briefed European parliamentarians last month.
First Minister Peter Robinson has said he appreciates the "support and encouragement Europe has given us".