The opposition says a new parliamentary system of government will allow Sarkisian, 63, to maintain huge influence under a new parliamentary system of government.
The protesters took to the streets after opposition leader Pashinian called on Armenians to stage rallies to prevent Sarkisian's political transition.
Pashinyan launched his 14-day protest campaign on 31 March from the second largest city of Gyumri to capital Yerevan as its final stop "to prevent Sargsyan's third term in office as the next prime minister and put an end to the rule of the Republican Party of Armenia (RPA)". The parliament where Sargsyan's party has majority will be electing the Prime Minister on April 17.
Several hundred people sat or lay down on pavements, blocking roads leading to the parliament building and universities.
Authorities beefed up police presence and put in place cordons which some protesters broke through.
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The witness noted they "were canoodling and being affectionate as she sat on his lap" claiming "they are 100% back together". They walked around the fields together in hugs and later Jeffries was seen resting her head on The Weeknd's shoulder.
During the rallies, dozens were injured, including opposition leader Nikol Pashinian - who called the protests - and a number of police officers.
Some built barricades using cast-iron benches and metal trash cans.
The incident comes amid protests against a recent change of government that the opposition sees as a move for ex-President Serzh Sargsyan to stay in power.
Under the new constitution adopted in referendum in 2015, Armenia is switching to a parliamentary system of government.
But Vahram Baghdasaryan, head of the RPA faction at the NA, assured that the next PM's election will take place in the parliament building.