Mr Erdogan said: “We will teach them international diplomacy.”
The Dutch government says such events would stoke tensions days before the Netherlands’ general election.
Foreign Minister Mevlut Cavusoglu tried to fly in but was refused entry.
Protests were also held on Sunday outside the Dutch consulate in Istanbul, where the Netherlands’ flag was replaced with a Turkish one, which was later removed.
Speaking at an awards ceremony in Istanbul on Sunday, Mr Erdogan said of the Netherlands: “They will certainly pay the price, and also learn what diplomacy is.”
Threatening to travel to rallies abroad himself, he added: “The West has clearly shown its true face in the last couple of days. What we have seen… is a clear manifestations of Islamophobia.
“I have said that I had thought that Nazism was over, but that I was wrong. Nazism is alive in the West,” he said.
But he thanked France for allowing Mr Cavusoglu to travel to the northern city of Metz to address a rally there on Sunday, saying: “France was not deceived by such games.”
Speaking in Metz, Mr Cavusoglu described the Netherlands as the “capital of fascism”.
He said of the Dutch ambassador, who is on leave: “We are saying that there is no need to come back to Turkey. He can’t come, he can’t enter.”
Ms Kaya also vented her anger at the Dutch after flying back to Istanbul from Cologne.
She said: “We were subjected to rude and rough treatment… Treating a female minister this way is very ugly.”
Dutch PM Mark Rutte said Mr Erdogan’s comment on Saturday that the Dutch were “Nazi remnants and fascists” was “unacceptable”.
He said it was “wrong” for Turkey to send ministers to the Netherlands, despite the Dutch government warning that it could inflame tensions in society.
He said Turkey had threatened sanctions and “we can never do business under this kind of blackmail”.
“We drew a red line,” he said.
The Dutch government is facing a severe electoral challenge from the anti-Islam party of Geert Wilders in its election on Wednesday.
Reports say the owner of a venue in the Swedish capital, Stockholm, has now cancelled a pro-Erdogan rally on Sunday that was to have been attended by Turkey’s agriculture minister. Sweden’s foreign ministry said it was not involved in the decision and that the event can take place elsewhere.
What is the row about?
Turkey is holding a referendum on 16 April on whether to turn from a parliamentary to a presidential republic, more akin to the United States.
So a number of rallies have been planned for countries with large numbers of expat voters, including Germany, Austria and the Netherlands.
However, Mr Erdogan’s supporters have found themselves blocked from holding these rallies.
Why are countries trying to prevent the rallies?
Austrian Foreign Minister Sebastian Kurz said Mr Erdogan was not welcome to hold rallies as this could increase friction and hinder integration.
Germany in particular has been critical of the mass arrests and purges that followed – with nearly 100,000 civil servants removed from their posts.