"There will be no new conditions of course," Verheugen told reporters on Wednesday during a final fact-finding trip to Turkey ahead of a European Commission progress report due on 6 October.
Verheugen pointed out that Turkey has made a start on improving cultural rights for its Kurdish minority under EU-oriented reforms, but must go further.
He said Kurdish language education and broadcasting were key areas for more action.
"I am satisfied [broadcasting] has started, with some delays, but I have to say what we have seen so far can only be the beginning," he told reporters during a visit to a village near the city of Diyarbakir in southeast Turkey.
The region has suffered in a 20-year conflict in which more than 30,000 people have been killed. EU observers claim the conflict facilitated human rights abuses that have long delayed Turkey's EU entry bid.
EU leaders will decide in December whether to give Ankara a firm start date for accession talks to the wealthy bloc, drawing on the Commission's progress report due on 6 October. Eventual talks would be expected to last for many years.
A swathe of reforms aimed at winning a start date for EU talks paved the way in June for the first, very limited Kurdish-language broadcasts on state radio and television.
The 20-year Kurdish insurgency
has claimed over 30,000 lives
Turkey's estimated 12 million Kurds say they also want Kurdish language education in schools. Many speak Kurdish, an Indo-European language unrelated to Turkish, in everyday life.
A few private Kurdish language courses have been allowed to open since April, but all schooling remains firmly in Turkish.
Verheugen said political and social tensions in the southeast were closely linked to economic conditions in the region, which has some of Turkey's poorest people, lowest investment and highest unemployment.
"You can't achieve political stability here without a better perspective for the people," he said, adding that the poverty would not in itself influence the European Commission's report.
He said Turkey also needed to step up efforts to help displaced Kurds return to villages destroyed in the conflict.
"You can't achieve political stability here without a better perspective for the people"
EU Enlargement Commissioner
"I think one should strongly support the wish of people to return to their villages," he said.
Tens of thousands of Kurds fled or were evacuated from their homes during the worst of the bloodshed, which largely subsided after the capture of separatist leader Abdullah Ocalan in 1999.
Violence has crept up again after Ocalan's Kurdistan Workers' Party (PKK) called off a six-year unilateral ceasefire in June.
A police officer and a security guard were killed early on Tuesday when suspected Kurdish guerrillas opened fire at a checkpoint outside Diyarbakir, where Verheugen stayed overnight, a security official said.