"A sniper opened fire from inside the police station and killed a police officer ... Who was sitting in a car parked 350-400 metres (yards) away," police spokesman Ashot Aharonyan wrote on Facebook.
Earlier Saturday, Armenia's security services gave the gunmen a deadline to surrender after dozens were hurt and arrested in overnight clashes.
"We are giving members of the armed group until 5:00 pm (1300 GMT) to lay down their arms and surrender," the Armenian national security services said in a statement.
"After the events of July 29, any opportunities to resolve the situation with the terrorists peacefully have been exhausted."
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Dozens were injured and 26 arrested in the early hours of Saturday after authorities broke up a rally near the police station, where the armed pro-opposition group has been holed up for almost two weeks with several hostages.
More than 70 people were taken to various hospitals around the capital to be treated for injuries including burns and broken limbs.
"Out of 73 injured people, 26 are still in hospital, including six policemen," health ministry spokeswoman Anahit Haytayan wrote on Facebook.
Journalists were among those hurt and a house caught on fire in the neighbourhood, a residential area.
Earlier Friday, police had exchanged fire with the gunmen, wounding two, who were taken to hospital under armed guard.
Armenian police told AFP that 165 people were detained in total during the overnight unrest, of whom 26 were later arrested.
The rest were released.
Authorities said they had launched a criminal probe into 23 of the protesters, including a member of the pro-Western Heritage party Armen Martirosyan.
On Saturday the area was generally calm, with several police officers manning the cordon thrown up since the hostage situation erupted and only letting through local residents after an ID check.