Erdogan at the weekend twice accused NATO ally Netherlands of acting like the Nazis, comments that sparked outrage in a country bombed and occupied by German forces in World War II.
Dutch Prime Minister Mark Rutte, who faces a major challenge from the far-right in a key general election Wednesday, said Erdogan's comments were unacceptable and it was Ankara that should apologise.
In apparent reference to Erdogan's comments, EU foreign policy chief Federica Mogherini and EU Enlargement Commissioner Johannes Hahn called on Turkey to "refrain from excessive statements and actions that risk further exacerbating the situation.
"Tt is essential to avoid further escalation and find ways to calm down the situation," their statement added.
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NATO chief Jens Stoltenberg also urged Turkey and its NATO allies to "show mutual respect, to be calm and have a measured approach to contribute to de-escalate the tensions".
The ministers had been seeking to harness the support of an estimated 400,000 people of Turkish origin living in the country ahead of the April 16 referendum on constitutional changes giving Erdogan greater powers.
The Turkish foreign ministry today summoned the Dutch envoy to Ankara for the third day in a row, handing two separate protest notes over The Hague's behaviour.
The Netherlands today also issued a new travel warning to Dutch citizens in Turkey, urging them to stay "alert across the whole of Turkey".
Denmark has also asked Turkish Prime Minister Binali Yildirim to postpone a visit planned for later this month.
The issue risks spiralling into a crisis with the EU as a whole, which Turkey has sought to join for more than half a century in a so far fruitless membership bid.
Erdogan, who has indicated he may attempt to address rallies in EU states in a move that could inflame the situation further, said Sunday that the West was showing its "true face" in the standoff.