Speaking at the rally in southern Adana province on Sunday, Kemal Kilicdaroglu said the party "will give every kind of support".
"If a minister of the Republic of Turkey is not allowed to enter her own consulate or embassy, please suspend [our] relations with the Netherlands," he said.
Turkey's National Movement Party (MHP) Chairman Devlet Bahceli also criticized the Netherlands, saying the Dutch move had blackened European values on freedom of speech and expression.
In a written statement, he added: "Turkey, with its government and the opposition, is an indestructible, impenetrable, impassable stronghold. The Turkish nation stands in solidarity against persecution."
On Saturday night, Family and Social Policies Minister Fatma Betul Sayan Kaya was blocked from entering the Turkish consulate in Dutch city of Rotterdam and was escorted to Germany by Dutch police.
In remarks made after returning to Istanbul on Sunday, Kaya said she suffered "harsh and rude treatment" at the hands of Dutch authorities.
Earlier on Saturday, the Dutch government also canceled the Turkish foreign minister's flight permit, which triggered a row between the two countries.
The ministers were due to meet Turkish residents ahead of the April 16 referendum on constitutional reforms in Turkey.