Here's a look at what's at the heart of the row and what's at stake for the parties in the conflict.
What is the dispute about?
Ankara has been dispatching ministers to various European countries to win votes from the Turkish diaspora ahead of a crucial referendum on April 16.
President Recep Tayyip Erdogan's government is urging the electorate to vote "yes", which would strengthen his powers and scrap the prime minister's post.
With an electorate numbering as many as 1.4 million in Germany alone, the voter base abroad is one that Erdogan cannot afford to ignore.
But the rallies have not been universally welcomed in the EU. Ties with Turkey were already frayed over various human rights issues -- especially the tens of thousands of arrests and sackings that followed the failed coup last July to topple Erdogan.
How did the row start?
It erupted on March 2, when the western German town of Gaggenau withdrew a hall rental agreement for a rally by Turkey's Justice Minister Bekir Bozdag, citing capacity problems.
Other local authorities followed suit, sparking fury in Ankara.
Erdogan lashed out at Germany, accusing it of "Nazi practices" in blocking the rallies.
The outburst met with consternation in Berlin.
Chancellor Angela Merkel signalled her government was not opposed to such rallies but stressed they must meet regulations.
Foreign Minister Mevlut Cavusoglu, after struggling to find a venue, finally addressed supporters from the balcony of the consul general's residence in Hamburg.
Turkey has since provided a list of upcoming campaign appearances in Germany.
Why did the crisis escalate?
Unlike Germany, The Netherlands simply refused to allow Cavusoglu's plane to land and expelled Family Minister Fatma Betul Sayan Kaya, after explicitly warning it did not welcome such rallies.
Prime Minister Mark Rutte said his government had sought to find a compromise for a "meeting of a small, private nature in the Turkish consulate or embassy", but this was "made impossible when we were threatened with sanctions".
Erdogan at the weekend twice accused the Netherlands of acting like the Nazis, comments that sparked outrage in a country bombed and occupied by German forces during World War II.
With the far-right mounting a major challenge in the Netherlands' general election on Wednesday, Rutte is in no mood to indulge Ankara.
He has insisted Erdogan's rhetoric is unacceptable and that it's Ankara that should apologise.
Why doesn't Turkey try to calm everyone down?
Analysts believe Erdogan may be playing to the gallery.
"Erdogan is looking for 'imagined' foreign enemies to boost his nationalist base in the run-up to the April 16 referendum, having run out of domestic adversaries he can cast as the 'enemy of the people'," said Soner Cagaptay, director of the Turkish Research Programme at The Washington Institute.
"It's as simple as that and the Dutch walked into this trap. They should have just ignored the pro-Erdogan rally. By blocking it, they may have given Erdogan a lifeline to eke out a victory in the referendum," Cagaptay added.
Where is the EU in all this?
Austrian Chancellor Christian Kern called for an EU-wide ban on such rallies, saying it would help take pressure off individual countries.
But Merkel's chief of staff Peter Altmaier noted that while the EU as a whole can decide on holding off on further membership negotiations with Turkey, he "has doubts" on whether they should jointly decide on a rally ban.
Is there a way out of the crisis?
For Marc Pierini, the EU's former envoy to Turkey, "in the short-term, there is no way out of the crisis because the referendum's outcome in Turkey is very tight and the leadership will do everything to ramp up the nationalist narrative to garner more votes".
"In the medium-term, one can hope that the fever will subside. Yet, bridges have been burned at a personal level: using a 'Nazi' narrative is the most extreme (insult) one can possibly use in EU politics and will most probably prevent any summit meeting between the EU and Turkey for a while," he warned.
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