Some 3.4 million Turks living abroad are eligible to vote in the runoff between incumbent Recep Tayyip Erdogan and challenger Kemal Kilicdaroglu.
Around 1.5m registered Turkish voters in Germany have until May 24 to cast their vote in the second round of the election, which will take place in Turkey on May 28.
The election is one of the most contentious in recent times, as witnessed by queues of voters at the Turkish embassy in Rome despite the rainy weather.
Turkey's ambassador to Rome, Ömer Gücük, was the first to cast his vote.
Turks in Italy will be able to vote on May 20, 21 and 22 at the Embassy in Rome and at the Consulate General in Milan.
In Spain, Turkish citizens have also started voting. The ballot papers from Madrid and Barcelona will be flown to Turkey by Turkish Airlines scheduled flights accompanied by diplomatic couriers on the morning of May 23.
In the first round of the elections, 3,510 out of 5,838 voters registered in Spain cast their ballot.
The show must go on
Meanwhile, the candidates continue campaigning.
Secular opposition leader Kemal Kilicdaroglu has vowed to send back millions of migrants in a strident message aimed at winning the backing of an ultra-nationalist who helped push last weekend's presidential vote to a runoff.
Turkey has taken in millions of migrants from neighbouring Syria mainly due to that country's civil war but also more recently because of the devastating earthquake that struck both countries in February.
In the first round last Sunday, the popular opposition leader came almost five points behind President Recep Tayyip Erdogan, the best opposition performance in Erdogan's two-decade rule.
But it fell short of expectations set by pre-election polling and left the opposition visibly depressed.
The 74-year-old has since revamped his campaign team and toughened his message to win over Turkey's right-wing voters in the May 28 runoff.
For his part, Erdogan took his campaign to Adiyaman, one of the worst-affected cities in the earthquake.
He told a rally that his opponent said Kilicdaroglu should apologise for his party members' rhetoric against quake victims.