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.

Axar.az reports that 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 is due to run until 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).

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.