Serzh Sarkisian took up the new position after stepping down from the presidency after serving two five-year terms.
Opposition MP Nikol Pashinyan, who has been leading the protests, has insisted that Sarkisian should resign as PM.
Here are profiles of the two key players in this developing story:
Sarkisian: balance abroad, corruption at home
A shrewd former military officer, Sarkisian has led Armenia since 2008 but has held high posts in the South Caucasus country ever since 1991, when the country became independent following the collapse of the USSR.
The 63-year-old began his political career when war erupted in the late 1980s with neighbouring Azerbaijan over his native Nagorno-Karabakh region, a conflict that is now frozen but technically unresolved.
He headed the mountainous region's self-defence forces between 1989 and 1993 and has since played a key role in negotiations over the area.
Sarkisian has said his experience in regulating the Nagorno-Karabakh dispute is one of the reasons he should remain in power.
In foreign policy, Sarkisian has remained a close ally of Armenia's former master Russia but has also been able to maintain relatively warm relations with the European Union.
"He has been able to keep Armenia's age-old balance between the West, Europe and Russia which is unprecedented in the post-Soviet space," said sociologist Gevorg Pogosyan.
At home, however, corruption in the police and judiciary as well as poverty has left an increasing number of Armenians dissatisfied with Sarkisian's rule.
"People took to the streets because of poverty, unemployment, corruption and because nothing is changing," Tatuk Hakobyan said.
All of Armenia's parliamentary and presidential elections under his rule have been accompanied by opposition-led protests.
"There is huge discontent in society," sociologist Pogosyan told AFP.
"He has infringed on the tradition that exists in our country: all previous presidents have left power on time, he promised he would too."
Pashinyan: from fugitive to leader
A fortnight ago, few in Armenia would have believed that opposition leader Nikol Pashinyan could bring tens of thousands of people out onto the streets of Yerevan and other cities, paralysing traffic and disrupting businesses.
Before these protests, Pashinyan was most closely associated with the tragic events of 2008, when 10 people died in clashes between police and supporters of Sarkisian's opponent in a presidential election.
He directed street demonstrations at that time and was put on a wanted list following the deaths.
The father-of-four went into hiding but in 2009 turned himself in, though was released in 2011 under a prisoner amnesty.
A former journalist, the 43-year-old later set up the Civil Contract party, which entered parliament last year as part of the opposition coalition Way Out.
With his fiery rhetoric and penchant for asking awkward questions, Pashinyan has proved a thorn in the side of Sarkisian's ruling Republican Party.
After being injured along with dozens of others at a protest on Monday, he has appeared at subsequent demonstrations with a bandaged arm and bruises under his eyes.
"Pashinyan differs from the majority of opposition figures in that he is daring, he's not afraid, he's creative, he's got a quick wit and stamina," Pogosyan said.
It is these characteristics which make Pashinyan appealing to young Armenians who grew up after the collapse of the Soviet Union, Pogosyan added, though older generations have also turned out for the street protests.
"People go to him because they are confident he's not going to make secret deals with those in power, he won't betray the movement," Pogosyan told AFP.
Analyst Aleksandr Iskandaryan said the opposition in the country had been crushed and Pogosyan was its sole figurehead.
"He has managed to personify (this movement)...Today the opposition in Armenia is him," Iskandaryan told AFP.
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