He said on Tuesday signing the protocol would be the "first significant step in normalising relations between the Cyprus Republic and Turkey".
Cyprus is the only European Union member with which Turkey has no formal diplomatic ties.
"Turkey must sign the protocol extending the customs union to all new EU member states, including Cyprus, before 3 October, when it is set to commence accession negotiations," Papadopoulos said in Nicosia before leaving for Brussels where he will also meet Greek Prime Minister Costas Karamanlis.
Turkey hopes to start talks on joining the EU in October after winning a green light from EU leaders in December, but the bloc has said Ankara must sign the agreement to cover Cyprus first.
De facto recognition
The EU expects Turkey to fulfil its commitment to sign the adaptation Protocol of the Ankara Agreement, an updated version of an already-existing customs agreement between Turkey and the EU, taking into account the bloc's 10 new member states which joined last year - including Cyprus.
While Turkey insists that extending the customs accord to Cyprus does not amount to official recognition of the Mediterranean island state, the EU says it amounts to de facto recognition.
Cyprus has been divided since 1974 when Turkey occupied its northern third following a Greek Cypriot coup seeking to unite the island with Greece.
"Turkey must sign the protocol extending the customs union to all new EU member states, including Cyprus, before 3 October when it is set to commence accession negotiations"
The Turkish Republic of Northern Cyprus (TRNC) is only recognised by Ankara.
A divided Cyprus joined the EU on 1 May last year, a week after Greek Cypriots rejected a UN reunification plan in a referendum. Turkish Cypriots had voted for the plan.
Ankara first applied to join the EU in 1963. The EU decision to finally start entry talks has sparked fierce debate over whether the bloc can take in a country with such vast economic, cultural and religious differences.
EU leaders have made it clear that, while membership talks can start this year, it will take at least a decade before Turkey can actually hope to join the EU.