Rutte said there had been discussions with the Turkish authorities to try to find a way to hold a smaller-scale meeting in a Turkish Consulate or Embassy.
Rutte said that while the Netherlands and Turkey could try to find "an acceptable solution", Turkey was not respecting the rules relating to public gatherings.
Dutch political leaders hit the campaign trail Saturday, criss-crossing the country to woo voters ahead of next week's elections now overshadowed by the bitter row with Turkey.
As Anadolu Agency reports, Kaya now resides in Germany, so she will come to Rotterdam by the land transport.
It then transpired a second Turkish official, minister for the family affairs Fatma Betül Sayan Kaya was heading to the Netherlands by auto from Germany.
The police would not confirm anything to AFP, and calls to the Dutch foreign ministry for comment went unanswered.
They were "crazy remarks", Rutte told reporters as he campaigned for re-election in Wednesday's polls in The Netherlands.
Semi driver killed by smoke from Kansas wildfire
Greg Abbot issued a statement Monday night saying he was sending state resources to the area to assist in fighting the fires. Jim Inhofe and James Lankford of Oklahoma planned to visit the northwest part of the state Friday to discuss the wildfires.
President Erdogan reacted to the ban on his foreign minister by threatening to block Dutch flights.
But it said Cavusoglu's threat hours earlier of political and economic sanctions if travel permission were withdrawn made the search for a reasonable solution impossible.
Cavusoglu was due to address Turkish expatriates in Rotterdam to win support for an April 16 referendum vote on the Turkish Constitution.
The town of Hoerbranz, in Austria, cancelled a meeting with a former Turkish minister because it had falsely been labelled as a book presentation.
Many in Europe worry that Erdogan is capitalising on fears following a failed coup attempt in July to push through a more authoritarian system with few checks on his power. Germany has been critical of the mass arrests and purges that followed - with almost 100,000 civil servants removed from their posts.
Erdogan is looking to the large number of emigre Turks living in Europe to help clinch victory in next month's referendum and give him sweeping new powers.
Turkey is a key partner in an arrangement attempting to limit the movement of migrants into the European Union, but has threatened to "open the gates" if the European Union reneges on commitments to provide aid, visa-free travel for its nationals and accelerated membership talks.