Both presidents were said to have expressed concern over the increasing political tension in Armenia.
As noted in delegation, the conflict must be resolved quickly through negotiations.
Hours after Prime Minister Serzh Sarksyan stormed out of talks with him, anti-government protest leader Nikol Pashinyan has been detained on Sunday.
But instead security forces intervened using stun grenades and began dispersing the crowd in Yerevan's suburban Erebuni district. The key person in the country is the Prime Minister.
"We are all citizens of the Republic of Armenia". Opposition protesters had hoped the meeting would help overcome the impasse.
"'Our main goal remains the stability, as well as the maintenance of normal life in the country", the first deputy prime minister. But Brussels is anxious that today's meeting of the leader of the protesters Nikol Pashinian and Prime Minister Serzh Sargsyan has not helped to reduce tensions.
"This is not a dialogue, this is blackmail".
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"This is not a dialogue; this is blackmail, I only can advise you to return to a legal framework. otherwise, you will bear the responsibility", Sargsyan replied.
"You don't understand the situation in Armenia".
Note to Readers: Today is the tenth day of protest in Armenia calling for the resignation of Serzh Sargsyan as prime minister and the transfer of power out of the hands of the ruling Republican Party of Armenia to the people.
Protesters have accused Mr Sargsyan of clinging on to power following his appointment as Premier this month, when he stepped down from the presidency after serving two five-year terms.
According to Armenia's amended constitution, approved in a national referendum in 2015, Armenia has switched the government from a semi-presidential to a parliamentary system making the presidency largely ceremonial and strengthening the office of the prime minister.
"My Step" initiative leader, opposition Civil Contract Party Political Council member, and National Assembly (NA) "Way Out" (Yelk) Faction head Nikol Pashinyan on Friday informed that on Saturday they will continue their protest actions of blocking streets and avenues.