Former colonial master Denmark became the first country in the world to recognize same-sex unions in 1989 and legalized gay marriage in 2012, but the issue remains controversial in the deeply-religious Faroe Islands.
"The political parties have found it very hard to take a decision on a party level," said Sveinur Trondarson, editor of Faroese newspaper Dimmalaetting.
Instead, the main parties had chosen to label it as an "ethical" issue, meaning lawmakers were "free to vote as they like," he said.
The ruling centre-right government has been prevented by one of its smaller coalition members, the Christian Centre Party (Midflokkurin), to put same-sex marriage to a vote in parliament.
A recent poll showed 64 percent of Faroe Islanders were in favour of civil unions for gay people and this year's gay pride festival in Torshavn, the capital, drew around 6,000 people.
Prime Minister Kaj Leo Johannesen called the election on July 29, three months before an election deadline of October 28.
The conservative-liberal Union Party (Sambandsflokkurin) leader was embroiled in controversy earlier this year when a probe found that he lied to parliament about a contract to build a subsea tunnel between two islands.
A Monday poll showed a narrow lead for the leftist opposition, led by the social democratic Javnadarflokkurin party.
The Danish question
But Faroese politics can be hard to predict since the parties in addition to the left-right scale also attract votes based on the thorny issue of whether the territory should remain part of Denmark.
The social democrats have campaigned on raising more tax revenue by auctioning fishing quotas and taxing fish farming.
The Faroe Islands are not part of the EU and salmon exports to Russia have soared after Russia last year slapped a ban on food products from the bloc.
The opposition has also criticised the government for cutting taxes for high income earners.
Polling stations in the overseas Danish territory opened at 10am CEST and were set to close at 10pm.
The archipelago, with 48,000 inhabitants and around 70,000 sheep, has been autonomous from Denmark since 1948 - though foreign affairs and defence are still the domain of Copenhagen.
The Faroe Islands' economic output reached 14.7 billion kroner (1.97 billion euros, $2.22 billion) in 2013.
It is heavily dependant on fisheries, which account for 95 percent of exports, and also receives an annual 650 million kroner subsidy from Denmark.