Erdogan reacted angrily by likening the ban to Nazism, saying "they are the vestiges of the Nazis, they are fascists".
Tensions between the North Atlantic Treaty Organisation partners have been growing over the weekend after the Dutch government barred Turkey's foreign minister from flying to Rotterdam. "These are the remains of Nazis, they are fascists", he added.
Erdoğan is campaigning for expatriate voters' support of an April referendum that would change Turkey's government from a parliamentary republic to a presidential one and expand his powers over the budget and appointments of key officials.
Turkish television reported that Kaya was stopped by Dutch police some 30 metres short of the consulate in Rotterdam.
Cavusoglu was to fly to Rotterdam on Saturday after he was barred from addressing a Turkish rally there.
The country's Turkish population "are not your captives", Çavuşoğlu warned the Netherlands in an interview with CNN Turk earlier on Saturday.
Erdogan is looking to expats living in Europe to help him win next month's referendum.
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Mr Cavusoglu had threatened economic sanctions against the Netherlands if his landing rights were rescinded, after he had been forced to address Turkish citizens in Hamburg from an embassy balcony after local Germany authorities cancelled rallies there citing public safety. A threat of sanctions from Turkey if Cavusoglu were denied entry "made a reasonable solution impossible", he said.
Mr Erdogan told the crowd back in Turkey: 'You can stop our foreign minister's plane all you want, let's see how your planes will come to Turkey from now on, ' Mr Erdogan told booing crowds.
Mevlut Cavusoglu said he would travel to Rotterdam on Saturday despite "all obstacles and despite all the racist speeches".
Rutte said it had been a tough decision given Turkey was "a North Atlantic Treaty Organisation ally", but he insisted: "I really think we made the right decision here". The Dutch government has no objection to meetings in our country in order to inform them about that.
Several German municipalities canceled similar political events last week, barring Turkish officials from rallying support among the country's Turkish politician, some 1.4 million of whom are eligible to vote in the upcoming referendum.
The ban drew strong criticism from the Turkish government.