But the rally was banned for security reasons, and the minister's plane was then refused permission to land.
Dutch Prime Minister Mark Rutte said the remark was "way out of line".
"It's a crazy remark, of course," Mr Rutte said.
Turkey has summoned the Dutch charge d'affaires to the foreign ministry in Ankara for an explanation.
In a strange twist, Turkey's family minister will attempt to travel by land to the Dutch city of Rotterdam, Turkey's state-run Anadolu news agency said.
Fatma Betul Sayan Kaya is in Germany for separate meetings but plans to head to the Netherlands later, despite having her meetings there cancelled.
'Reasonable solution impossible'
President Erdogan reacted to the ban on his foreign minister by threatening to block Dutch flights.
He said: "Ban our foreign minister from flying however much you like, but from now on, let's see how your flights will land in Turkey."
Foreign Minister Mevlut Cavusoglu also warned Turkey would impose heavy sanctions if his visit were blocked.
Mr Rutte warned in a statement (in Dutch) that the Turkish threat of sanctions made "the search for a reasonable solution impossible".
Mr Rutte also stressed that Dutch officials had earlier discussed whether the planned rally with Mr Cavusoglu could be private and "smaller-scale" and held in a Turkish consulate or embassy.
The Netherlands "regrets the course of events, and remains committed to dialogue with Turkey," the statement added.
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