Speaking at a political rally in Bursa on Thursday, the Turkish leader vowed to "eradicate Twitter" following last year's anti-government demonstrations, which featured organisers utilising the social media website.
S&D group leader Hannes Swoboda accused Erdoğan of having "lost all sense of direction and balance", adding , "Banning a social media network with 10 million users in Turkey is nothing short of a blatant attack on freedom of speech.
"Turkey, as a country in the process of accession talks to join the European Union, has a duty to respect fundamental human rights. Freedom of speech is a core right of people and Erdoğan's authoritarian oppression of it will not succeed," warned the Austrian MEP.
He continued, "Erdoğan may not care what the international community thinks about him, but the international community cares about the rights of the Turkish people.
"I recommend he takes a look at article 26 of the Turkish constitution; emergency anti-terror legislation does not justify curtailing the rights of 10 million people."
Hélène Flautre, who is co-chair of parliament's delegation to the EU-Turkey joint parliamentary committee, agreed, saying, "The move by Erdoğan to block Twitter is an absurd attack on fundamental rights and freedoms in Turkey.
"This latest anti-democratic manoeuvre only compounds concerns about the new internet law, which finds here its first application."
The country's internet law, passed in early February, grants powers to Turkey's telecommunications authority to block websites without first seeking court approval and forces internet service providers to store data related to users' online activities and make it available to the authorities if requested.
"There was already major concern about the crisis hitting the democratic institutions in Turkey, with revelations of alleged intervention in media and the judiciary by the government," she explained, adding, "We would strongly urge the EU to engage immediately with the Turkish authorities to prevent further democratic backsliding ahead of the forthcoming elections."
Ria Oomen-Ruijten, parliament's rapporteur on the resolution on the 2013 progress report on Turkey, also voiced her criticism of Erdoğan's Twitter crackdown, saying, "Blocking social media is unacceptable in a functioning democracy and rule of law. I call on the Turkish government to address this issue without delay. Turkish citizens should be able to express their opinion both offline and online."
"Turkey is backtracking instead of taking steps forward. Measures that limit freedom for the citizens and the press have no place in a modern society and democratic rule of law," the Dutch deputy concluded.
And Greens/EFA member Ska Keller was equally critical, saying, "In blocking Twitter, Erdoğan is also blocking the freedom of expression in Turkey. It is a clear attack on democracy with the single aim of silencing all criticism against him.
"The commission should send out a strong message to the Turkish government that undermining freedom of expression is not acceptable."
In a statement responding to the situation, enlargement and European neighbourhood policy commissioner Štefan Füle said, "The ban on the social platform Twitter.com in Turkey raises grave concerns and casts doubt on Turkey's stated commitment to European values and standards.
"Freedom of expression, a fundamental right in any democratic society, includes the right to receive and impart information and ideas without interference by public authority. Citizens must be free to communicate and choose freely the means to do it. This obviously includes access to the internet.
He concluded "Open debate promotes transparency and accountability and ultimately reinforces democracy; such debate needs to be strengthened everywhere, including in Turkey."