Witnesses said they had seen police fire tracer rounds above the heads of protesters and lob tear gas into the crowd on Saturday.
Demonstrators armed with metal bars and petrol bombs torched cars and looted shops.
Emergency laws have banned all public meetings and restricted media reporting.
Levon Ter-Petrosian, the defeated presidential candidate, has blamed police brutality for the violence.
Heikki Talvitie, a special envoy for the Organisation for Security and Cooperation in Europe (OSCE), when asked if a negotiation between the two sides was possible, said: "In all likeliness, this kind of dialogue between Ter-Petrosian and the government, at the moment, is not possible."
However, he said there was a possibility that both sides could negotiate in the days to come.
Talvitie said: "Let's not exclude it from the future."
Earlier, the envoy flew into Yerevan on Sunday and met Kocharian and Sarkisian for talks.
Talvitie also met the opposition groups in order to break the deadlock.
A US state department spokesman said Washington was sending Matt Bryza, deputy assistant secretary of state, to help "facilitate discussions" between the government and opposition.
But he stressed Bryza would not carry out "formal mediation".
Meanwhile, analysts say Armenia is heading for a period of uncertainty as neither side has shown much willingness to back down.
Petrosian has told his supporters not to rally during the 20-day emergency period.
However, he said he wass prepared to continue the protests afterwards.
A western diplomat said: "Petrosian is very determined and very charismatic. He'll find it difficult to step back from this now."
February's presidential poll saw Sarkisian win 53 per cent of the vote and Petrosian 21.5 per cent.
The OSCE described the election as flawed but sufficient enough for Armenia to fulfil its international obligations.
Kocharian and Sarkisian have presided over a period of economic growth, but detractors accuse their government of corruption and nepotism.
Petrosian was Armenia's first president after it broke away from the Soviet Union.
Although street demonstrations forced him to resign in 1998, he is still supported by many who want an alternative to the current government.