The warning on Wednesday came following the European Parliament's subcommittee on human rights delegation visit to Turkey this week (16-18 May).
The delegation was led by Dutch ALDE member Marietje Schaake, accompanied by German Socialist MEP Arne Lietz and his Portuguese colleague Liliana Rodrigues.
Its main focus was the human rights aspects of the EU-Turkey agreement reached on 18 March to better manage migration flows, as well as the general rule of law situation in Turkey, including the conflict in the south east, freedom of expression and of the media.
The visit took place a month following the adoption of Parliament's critical annual report on Turkey and only days after debates on visa liberalisation in the assembly.
MEPs cautioned that Parliament would play a "responsible and principled" role by only referring the visa liberalisation agreement for vote once all remaining requirements are fulfilled.
The delegation said these include amending anti-terrorism legislation and establishing data protection in line with European standards.
This is Parliament's official position and was also reiterated during the visit.
The delegation met with deputy Turkish ministers and officials of the ministry of EU affairs, interior and justice, members of the Turkish Grand National Assembly (TGNA), the Turkish ombudsman, as well as representatives of civil society and international agencies and journalists.
The three MEPs also visited the editors-in-chief of Cumhuriyet and the Hürriyet, two of the major independent Turkish newspapers.
Members said they ended the visit on Wednesday "recognising the critical moment for politics" in Turkey while the TGNA debated a motion to lift the immunity of certain MPs and an important upcoming AK party congress on the new leadership.
The MEPs said that all meetings took place in a "frank and open" atmosphere with all Turkish counterparts and it was agreed to work closely on issues of mutual interest with the Turkish Parliament.
On Wednesday, Marietje Schaake, who chairs the subcommittee delegation, told this website, "The deal between the EU and Turkey has put a new spotlight on the relations between the two.
For the European Parliament it is essential that core principles on respect for international law, the rule of law and human rights are upheld. "
"Whether it relates to the treatment of refugees, to the anti-terror laws or press freedom, only a values based assessment will ensure a credible and durable relationship, which serves people in Europe and Turkey".
A press conference concluding this visit was due to take place later on Wednesday in Istanbul.