Considering its status as the unofficial soundtrack to one of the most tense and emotionally ambivalent summers in recent Georgian history, the song Sakartveloa by rock band Mgzavrebi is surprisingly simple.

Its chorus, shouted at increasing volume, translates as “This is Georgia” or “It’s Georgia” – Sakartvelo being the country’s Georgian name, and the a being short for aris, meaning “is”.

In May and June this year, there were big street demonstrations in Tbilisi, capital of the former Soviet state, which lies between Turkey and Russia, against a controversial foreign influence law. Protesters see it as a sign of democratic backsliding.

Then came Georgia’s first ever European Championship: four delirious football matches that involved a nail-biter against Turkey, a thrilling victory over Portugal and an emphatic defeat at the hands of champions Spain.

Released just ahead of the Euros, Sakartveloa helped ground Georgians throughout that emotional rollercoaster. Circling around the same four chords, it has been likened to a Georgian Three Lions.

Its only real theme is Georgia itself: in two short verses, it describes how Georgians live “in praise of the past”, “arguing about the present” and “in hope for the future”.

“We always wanted to write a song about Georgia but it wasn’t easy, as there are already so many beautiful ones out there,” Mgzavrebi bandmembers tell the Guardian in an exchange of text messages. “When our football team qualified for Euro 2024, this gave us the perfect inspiration.”

Georgia may have exited the Euros more than a month ago, but Sakartveloa has outlived the competition. Blasted out in taxis, cafes and restaurants, it is still as omnipresent in the capital as the Georgia flags hanging from windows and graffitied on walls around Rustaveli Avenue, the street central to the protests of the past few months.

“It’s still incredibly popular,” the band says. “We think it’s the emotion it brings out in people, making listeners feel tears of happiness, pride and nostalgia, especially those [Georgians] living abroad.”

The song is likely to ring even louder around Georgian streets and market squares in the coming weeks, as the Caucasus country shapes up for critical parliamentary elections on 26 October. Activists say that what is at stake in the vote is not only Georgia’s path of accession to the EU, which up to 80% of Georgians support, but also its independence from the Russian sphere of influence.

The ruling Georgian Dream party, which came to power in 2012 on a promise to maintain the country’s EU-bound trajectory but has recently switched to more anti-western rhetoric, has signalled it might ban political opposition groups if it emerges triumphant.

President Salome Zourabichvili, who has become increasingly alienated from the government over the past few months, has framed the vote as a referendum between “Europe or Russia”, and “freedom or slavery”.

In this divisive climate, Sakartveloa’s appeal has been its ability to briefly transcend politics and crowd a common cause. Tinatin Bokuchava, chair of the United National Movement – Georgia’s main opposition party – believes the song’s message can fuel a concerted effort to vote out the government.

“Sakartveloa represents the spirit of Georgia, a country with so much hope for the future and which can achieve incredible things when it comes together,” Bokuchava says. “I know that the same unity and hope will inspire the Georgian people to reject authoritarianism and embrace a democratic, prosperous and European future at the elections.”

Not everyone buys into the same optimistic reading. “The song’s lyrics are a compromise between the current government and the protesters,” says Nino Sharvashidze, an academic at Tbilisi State University who has worked on several election observation missions in Georgia. Compared with the songs that have come directly out of this summer’s protests, she says, Sakartveloa was relatively conformist and its optimism blind. Its message reminded her of the short-lived compromise between Poland’s Solidarity movement and the then communist government in 1980.

Mgzavrebi, a mainstream rock band founded in 2006, have so far declined to take sides in their country’s fierce political debates, and look unlikely to do so in the run-up to 26 October. This autumn, they will take their anthem to other politically tense regions of the globe, with a nine-tour date through Canada and the US that began on 18 September.

• Mgzavrebi play New York’s Melrose Ballroom on 3 October