Last week, the bearded 52-year-old led protesters towards the capital, Yerevan, from his diocese of Tavush, the home of four frontier villages, which the government has agreed to return to Baku.
Thousands joined the charismatic cleric on his six-day march in solidarity with Tavush residents.
As he led marching protesters to Yerevan, Galstanyan -- who suffers from varicose veins -- was frequently seen stopping on the roadside to bandage wounds on his bleeding legs.
The archbishop, who studied in Britain and Canada, denounced Prime Minister Nikol Pashinyan as a "liar" responsible for Armenian defeats and territorial concessions to Azerbaijan.
"We need a new government, a government of the people, a caring, suffering government, a government of reconciliation," he told demonstrators when he demanded Pashinyan's resignation during a recent rally in Yerevan.
"I am out fighting today because we live at a time of stolen joy and infamy... when all the borders of our homeland are in danger," he said.
Armenia and Azerbaijan had fought two wars for control of the breakaway Nagorno-Karabakh region, which Baku's forces recaptured last year from Armenian separatists who had held sway over the mountainous enclave for three decades.
The premier's decision to relinquish territory -- which was seized by Yerevan in the 1990s -- for the sake of a peace deal with Azerbaijan to stabilise ties has sparked nationwide outrage.
In Yerevan, tens of thousands have taken to the streets, demanding Pashinyan's resignation.
Church backing?
Galstanyan has channelled the public anger and has secured opposition MPs' backing for his effort to initiate in parliament impeachment proceedings against the head of government.
Opposition parties would require the support of at least one independent or ruling party MP to launch the impeachment process and success would hinge on at least 18 lawmakers from Pashinyan's own party voting to unseat the leader.
Pashinyan, a former journalist, was propelled to power on the wave of popular protests he spearheaded in 2018 against corrupt Soviet-era elites.
Galstanyan is mirroring Pashinyan's 2018 protest tactics that include a combination of mass rallies and small groups of demonstrators blocking streets across the capital.
According to the Armenian constitution, lawmakers demanding a premier's impeachment must nominate their prime-ministerial candidate.
Galstanyan has not put himself forward but has signalled he could renounce his Canadian citizenship, which currently prevents him from running for office.
Independent analyst Vigen Hakobyan said the archbishop's protest movement is being "backed by the leadership of Armenia's Apostolic Church". It has long been at loggerheads with Pashinyan who promoted secularism in the country's schools.
Last week, the Church's Supreme Spiritual Council, which wields significant influence in the patriarchal country, described Galstanyan-led protests as "Armenians' righteous uprising."
Galstanyan was born in Armenia's second-largest city of Gyumri to Persian Armenians who had moved to the country from the tiny Iranian village of Sangibaran.
He graduated from the University of Leeds in England and later continued postgraduate studies of theology and bioethics at Canada's Concordia University.
Before returning to Armenia, he headed the diocese of the Armenian Church in Manchester and served as the Primate of the Church's Canadian diocese.