The complaints come even as Turkish President Recep Tayyip Erdogan himself has slammed European countries for not letting his ministers campaign on their soil for the April 16 vote on giving his office more power.
Erdogan kept up the criticism in an Istanbul speech on Sunday, denouncing the Netherlands and then singling out German Chancellor Angela Merkel.
"You are committing Nazi practices too," he said. "To whom? To my Turkish brothers and sisters in Germany."
"Those who advocate for a 'no' vote are faced with a series of obstructions," said Utku Cakirozer, a former journalist who is now a lawmaker for the opposition Republican People's Party, or CHP.
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While he, too, criticized moves by Germany and the Netherlands to stop Turkish ministers from campaigning to Turkish citizens abroad, Cakirozer said "our democracy bar has been lowered a great deal and needs to be raised rapidly."
Critics say it would give Erdogan too much control and further erode the democratic separation of powers in the country.
With opinion polls suggesting the outcome of the tight race could be determined by yet-undecided voters, "no" campaigners say they face an uphill battle because Turkey's TV channels are either pro-government or refrain from broadcasts critical of the government for fear of reprisals.