Turkish Foreign Minister Mevlut Cavusoglu, speaking at the opening of an ambassadors meeting, said he wanted more chapters in the accession talks to be opened "by lifting artificial obstacles to our EU membership".
A "chapter" is a specific area of negotiation, ranging on issues from human rights to economic cooperation. Cavusoglu did not specify which chapters he meant.
He also said Turkey expects "visa liberalisation for Turkish citizens to be provided immediately", a reference to EU commitments on visa-free travel for nearly 80 million Turkish citizens made in March under an EU-Ankara deal to curb migrants entering Europe.
Erdogan threatened in December to cancel the migrant deal, which has dramatically reduced the numbers crossing into Europe via Greece.
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The accession talks stalled after a failed coup in July by a rogue Turkish military faction was followed with a crackdown that saw mass arrests of not only officers but also journalists, activists, academics and others.
"We've played an important role in Europe's past and will do so in the future," Cavusoglu said, adding: "A Europe without Turkey is incomplete."
US-Turkey relations were also strained in the aftermath of the failed coup attempt, with Ankara accusing the Pennsylvania- based Islamic preacher Fethullah Gulen of being the mastermind behind the putsch.
But Cavusoglu said he thought relations would improve under incoming US president Donald Trump.
"We believe the US will not continue to make the same mistakes it has previously made," he said.
He repeated a demand for the United States to extradite Gulen and his top followers to Turkey -- request that has been made repeatedly since the thwarted July 15 coup.
Washington considers the YPG as an ally in the fight against the so-called Islamic State (IS) jihadist group in Syria.
"Turkey and the US have the potential to create positive effects in a wide geographical region," Cavusoglu said.
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