Austria however refused to sign the statement because it wants a complete freeze of Turkey's long-stalled process for joining the 28-member bloc, including negotiations that are currently underway.
"Under the currently prevailing circumstances, no new chapters are considered for opening," said the statement by the European Union presidency, which is currently held by Slovakia.
A "chapter" is a specific area of negotiations in the membership talks, on issues ranging from human rights to economic cooperation.
The development is likely to further strain EU ties with Turkey in the wake of the government's mass arrests and purges following the failed coup against President Recep Tayyip Erdogan in July.
It comes despite a promise by the EU in March to prepare to open new chapters at an "accelerated pace" as part of a landmark deal with Ankara to tackle the migration crisis.
The EU opened one new chapter in June, but this brings the tally to only 16 out of the 35 required for Muslim-majority Turkey to join the bloc. Only one chapter has been completed.
'Step in right direction'
EU divisions were on show with Austria leading calls for the accession process to be halted altogether over Turkey's post-coup crackdown.
The European Parliament last month also voted in favour of freezing the membership talks.
After Austria refused to sign up to Tuesday's statement, the Slovak presidency said it "notes the absence of a consensus" but that there was an "overwhelming majority" on the course of action.
Austrian Foreign Minister Sebastian Kurz said that Turkey "is moving away from the EU" and that the Netherlands and Bulgaria backed Vienna's call for a complete freeze.
"The text developed in the right direction, but it was not yet enough from my point of view," Kurz told reporters.
But he said the statement is "definitely positive", adding: "New chapters cannot be opened. That is at least a step in the right direction."
However, German Minister of State Michael Roth warned that "we shouldn't slam the doors in this difficult phase" despite "a regression" in the rule of law and media freedom in Turkey.
But at the same time, he said: "There has to be a clear signal of the European Union to... the citizens in Turkey who share our European values."
Turkey formally applied to become an EU member in 1987 and accession talks only began in 2005, even though Ankara's aspirations to become part of the bloc date back to the 1960s.