TEHRAN, Young Journalists Club (YJC) - Many of the demonstrators waved national flags and held up placards reading "Sarkisian is a dictator".
Some attempted to block roads in response to repeated calls by the leader of the protests, opposition MP Nikol Pashinyan to paralyze traffic.
Police said dozens of people were detained.
Since last Friday, opposition supporters have held rallies to denounce Sarkisian's efforts to remain in power as prime minister after a decade serving as president.
Opposition parties have criticized the 63-year-old leader over poverty, corruption and the influence of powerful oligarchs in the country of 2.9 million people.
The spokesman for Sarkisian's ruling Republican Party said the newly elected prime minister would not step down.
"We respects citizens' right to freedom of assembly but we rule out the possibility of the prime minister resigning," Eduard Sharmazanov told journalists late Thursday.
Human Rights Watch condemned the "arbitrary arrests" of demonstrators.
"One should not underestimate the challenges Armenia's police are facing in maintaining law and order, but the ongoing protests are no justification to arbitrarily detain people," it said in a statement.
Parliament elected Sarkisian as prime minister on Tuesday after he served a decade as president from 2008 under a new parliamentary system of government.
Controversial constitutional amendments approved in 2015 have transferred governing powers from the presidency to the premier.
In the biggest protest in Armenia in years, tens of thousands took to the streets over Sarkisian's election as prime minister on Tuesday night but the number of demonstrators has since dwindled.
Some 15,000 rallied in Yerevan on Thursday night.
Source: AFP