Complying with EU demands on issues such as respect of human rights, civil liberties and freedom of expression were part of the deal thrashed out in March between the EU and Turkey to help stem the flow of migrants into the EU.
But, speaking in Parliament, Dutch defence minister Jeanine Hennis-Plasschaert said Turkey still "has a lot of homework to do."
The deal offered to Turkey was "not just a present to President Erdogan or a concession but something from which we all will benefit, including human rights activists."
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European migration and home affairs Commissioner Dimitris Avramopoulos also said Turkey still needed to make progress but that he was optimistic that Ankara would give a final push to the necessary reforms by the end of June.
Even so, the official warned, "We are not watering down our standards."
Both were addressing MEPs in Strasbourg in a debate on Turkey's progress in meeting its obligations as part of the EU/Turkey visa liberalisation roadmap designed to give Turkish citizens visa free access to the EU's Schengen area from later this year.
The Turkish minister for EU affairs by saying he is losing hope of getting a deal on visa-free travel for Turks within Europe.
Bozkir said that his hopes of getting visa-free travel for Turkish nationals were "getting less and less".
He admitted to the BBC that the negotiations had reached a crucial phase, stressing that Turkey had already done enough.
Bozkir said changing anti-terror laws in Turkey would be impossible.
The EU insists that Turkey needs to narrow its definition of terrorism - as well as meet four other key criteria - to qualify for visa-free travel.
In Wednesday's parliamentary debate, Greens/EFA group MEP Ernest Maragall, a member of Parliament's delegation for relations with Turkey, spoke out in support of liberalising EU visa conditions for Turkish citizens to visit Europe.
But the Catalan MEP said that visa liberalisation should not be approved until the Turkish state complies with its obligations.
Maragall said, "Turkish citizens, like those of any other country applying for EU membership, should be able to travel, study, and work for and within the EU. But Turkey today is not fulfilling these obligations, to the detriment of Turkish citizens who'd like to exercise their rights.
"The facts are clear. In four key areas, Turkey is evidently failing to live up to its obligations."
Further comment came from Greens/EFA group Co-Chair Rebecca Harms, who said, "The clamp-down against all opposition by the Erdogan regime has reached new level. The sentencing of the journalists Can Dundar and Erdem Gül to long prison terms for criticising the government is the latest worrying development; the attack on Dundar in particular shows the deep division President Erdogan has created in Turkey."
She added, "The recent developments make clear that the EU cannot rely on Turkey alone for its refugee policy."
Far-right MEP Marine Le Pen described the idea of giving visa-free access to Turks as "absolutely crazy", adding that Erdogan was using migration as a "weapon" against the EU.
On Monday, the civil liberties committee said the EU "should make sure that all its requirements are met" before granting Turkey visa-free access to the Schengen area.