Observers say that President Milo Djukanovic faces stiff challenge from newcomer and economist Jakov Milatovic.
Polling stations opened at 7am (05:00 GMT) and will close at 8pm (18:00 GMT). First unofficial results by pollsters, based on a sample of the electorate, are expected about two hours later.
The outcome of the contest will likely determine the balance of power in the Balkan nation ahead of a snap parliamentary vote due in June, following months of gridlock after the government collapsed in August.
Montenegro’s president, elected for a five-year term, has a mostly ceremonial position and most of the political power resides with the prime minister.
The run-off vote on Sunday is being held after none of the contenders won majority support in the first round of voting two weeks ago. Some 540,000 people are eligible to vote in Montenegro, a country of 620,000 located in the Balkan peninsula and by the Adriatic Sea.
Djukanovic, 61, has dominated Montenegro as president or prime minister for 33 years, since the start of the collapse of the now-defunct federal Yugoslavia. He led Montenegro to independence from Serbia in 2006.
Under Djukanovic’s leadership and his party, Montenegro joined NATO, kick-started the negotiating process for EU membership and moved away from Russia’s influence.
Opponents have long accused the former communist and his Democratic Party of Socialists (DPS) of corruption, ties with organised crime and running the small Adriatic republic as their fiefdom – allegations they deny.
Nikola Zarkovic, a student, said he hoped the vote would benefit everyone in the country, which mainly relies on revenue from tourism along its scenic coast.
“The free and independent Montenegro will be victorious, as always,” he told Reuters news agency after voting in a school inside one of drab communist-era apartment blocks in Podgorica.
Milan Popovic, a 64-year-old teacher said he was “expecting a good day … a historic day”.
“As do most of the people, I want changes for the better,” he added, according to Reuters.
Tight race
Djukanovic’s rival is Jakov Milatovic, 37, a former economy minister and the deputy head of the Europe Now movement that has pledged to curb corruption, improve living standards and bolster ties with the European Union and fellow ex-Yugoslav republic Serbia.
Djukanovic wound up with 35.37 percent of the vote in the first round of the election on March 19, with Milatovic on 28.92 percent, necessitating a run-off because neither garnered a 50 percent majority. Analysts have predicted a tight race in the run-off.
Sunday’s vote follows a year of political instability in which two governments were felled by no-confidence votes. It was also marked by a dispute between politicians and Djukanovic over his refusal to name a new prime minister.
On March 16, Djukanovic dissolved parliament and scheduled snap elections for June 11. Although the presidential post in Montenegro is largely ceremonial, victory in the election would bolster the chances of the winner’s party in June.
Montenegro has a legacy of bitter divisions between those who identify as Montenegrins and those who see themselves as Serbs and are opposed to the country’s independence.
The country joined NATO after a 2016 coup attempt that the Djukanovic government blamed on Russian agents and Serbian nationalists. Moscow dismissed such claims as absurd.
After Russia’s invasion of Ukraine last year, Montenegro joined EU sanctions against Moscow and expelled a number of Russian diplomats. The Kremlin has placed Montenegro on its list of unfriendly states.