Thousands of Armenians took to the streets in the capital Yerevan on Sunday in a fresh protest against Prime Minister Nikol Pashinyan's concessions to arch foe neighbour Azerbaijan.

The protests began in April, when the Caucasus nation's government agreed to hand back to Baku territory it had controlled since the 1990s.

On Sunday, several thousand protesters gathered in Yerevan's central Republic Square, outside government headquarters, an AFP reporter at the scene said.

But Pashinyan's rule remains unshaken, despite a challenge mounted by influential archbishop Bagrat Galstanyan.

In his address to the rally, Galstanyan called Pashinyan "a beggar" who sought to secure peace with Azerbaijan "at the price of his own people's humiliation."

He urged parliament to convene for an extraordinary plenary session on Tuesday to impeach the premier.

"On the people's demand, lawmakers must vote for the government's resignation and the formation of a new one," he told the crowd. An interim government must then call early parliamentary elections, he added.

Later in the evening, protesters staged a march towards parliament building.

"We must act, we must increase pressure on Pashinyan," said one of the demonstrators, 20-year-old student Shushan Sargsyan.

"The very existence of our country is at stake," said David Ohanyan, 36.

"Armenians must all realise this and take to the streets."

Galstanyan has temporarily stepped down from his religious post to run for prime minister.

He is not however eligible to hold the office under Armenian law because he has dual citizenship with Canada, leading to speculation as to how he might resolve this problem.

Last week, Armenia officially returned control over four border villages it had seized decades earlier to Azerbaijan, a decision Pashinyan has defended as a step to securing peace with Baku.

The Caucasus rivals have fought two wars for control of the Nagorno-Karabakh region, which Azerbaijan recaptured last year from Armenian separatists who held sway over much of the mountainous enclave for three decades.