(This April 11 story has been corrected in second paragraph to show overseas voting has finished)

A billboard carrying a picture of Turkish President Tayyip Erdogan and a slogan reading, "People say Yes, the Republic gets stronger", is pictured ahead of the constitutional referendum in Istanbul, Turkey, April 11, 2017. REUTERS/Murad Sezer

ANKARA (Reuters) - Turks living overseas are turning out in greater numbers to vote in a referendum on changing the constitution to create an executive presidency, President Tayyip Erdogan said on Tuesday, a development that pollsters say could benefit him.

Voters in Turkey will go to the polls on April 16 to decide on the referendum that would give Erdogan sweeping new powers. Voting for expatriate Turks began as early as late March in some countries and finished on Sunday.

The referendum campaign has brought a rapid deterioration in relations with some of Turkey’s European allies over the banning of some rallies by Turkish ministers in the Netherlands and Germany on security grounds, something Erdogan has denounced as “Nazi-like” tactics.

A high turnout abroad is likely to boost Erdogan, pollsters say, citing past elections, but at home it could hurt him as opposition voters traditionally make up a bigger proportion of those who tend to shun the polls on an election day.

“There is an amazing explosion of votes abroad. Around 1.42 million votes have been cast,” Erdogan said at a ceremony in the southeastern city of Sanliurfa, calling on his supporters to flood the ballot box with “yes” votes in the referendum.

The figure Erdogan cited suggests a turnout of around 50 percent, based on the 2.88 million voters registered abroad in the last general election in November 2015, according to data from the High Electoral Board (YSK).

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In that election the turnout was around 40 percent among expatriates, with 56 percent of those votes being cast for the AK Party, which Erdogan founded more than a decade ago.

Polls show a close race days before the referendum, putting the “yes” vote slightly ahead, but indicate that nearly half the country could reject the proposed constitutional changes.

Foreign vote results will be announced once the actual referendum is held on Sunday.

BITTERLY DIVIDED

One polling company, Mak Danismanlik, seen as close to Erdogan, said initial exit polls from abroad showed the “yes” vote at 62 percent. It said the only country where the “no” vote had prevailed was the United States. It did not say how many people it had polled or where the research was conducted.

Pollsters Gezici, whose research has tended to overestimate opposition support, forecast 82-83 percent voter participation domestically and a “yes” vote as high as 56 percent if the turnout is lower in Turkey.

The referendum has polarized the nation of 79 million. Erdogan’s opponents fear increasing authoritarianism from a leader they see as bent on eroding modern Turkey’s democracy and secular foundations.

Erdogan argues that the proposed strengthening of the presidency will avert instability associated with coalition governments, at a time when Turkey faces security threats from Islamist and Kurdish militants.

It was not immediately clear what the turnout in specific countries was, but in the November 2015 election, around 40 percent of the Turks in Germany cast their votes while the figure was around 45 percent in the Netherlands.

Germany’s Sueddeutsche Zeitung newspaper said Turks living there had cast 696,863 votes for the referendum, bringing turnout in Germany to 48.73 percent.