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Turks living in Germany began casting their ballots on Monday in a referendum that proposes changing Turkey's constitution to increase President Tayyip Erdogan's powers.

The controversial vote takes place amid increasingly strained ties between Turkey and Europe, home to an estimated 2.5 million Turkish citizens eligible to vote.

Bans on campaign rallies by Turkish officials in Germany and the Netherlands have prompted Erdogan to accuse European leaders of "Nazi methods".

German Finance Minister Wolfgang Schaeuble said on Sunday Erdogan's rhetoric was setting back integration in Germany by years and it would take years to repair the damage.

Germany has about 3 million people of Turkish background, including some 800,000 ethnic Kurds.

About 1.41 million are Turkish citizens eligible to cast ballots at the voting stations located mostly in Ankara's 13 consulates around Germany.

Erdogan argues the proposed strengthening of the presidency will avert instability associated with coalition governments, at a time when Turkey faces terrorist threats. Critics, including European leaders, say it will concentrate too much power in his hands.

Dozens of people lined up outside the Turkish consulate in Berlin to vote as a handful of supporters of Turkey's main pro-Kurdish opposition party, the Peoples' Democratic Party (HDP), held up protest signs.

One sign read: "6 million HDP voters are not represented at the ballot box."

Several HDP lawmakers have been arrested in Turkey.

Erdogan's critics say they worry that Turks in Germany opposed to him will refrain from voting to avoid repercussions for themselves or their families back home.

Agencies contributed to this report.