Two doctors and two nurses were held after entering a police compound seized by the assailants 10 days ago to treat two gunmen injured in clashes.
"The doctors who went into the captured territory to assist two members of the armed group who refused to go to hospital have been taken hostage," police spokesman Ashot Aharonyan wrote on Facebook.
"The police are taking steps to free the doctors through negotiations."
A health ministry spokesman said later on Facebook that one of the nurses had been freed.
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Gunmen -- supporters of fringe jailed opposition leader Zhirair Sefilyan -- stormed a police building in Yerevan on July 17, killing one officer, taking several more hostage and seizing a store of weapons.
Over the weekend they released the final four police officers being held captive but remained holed up inside the police building surrounded by law enforcement officers.
The group has demanded the resignation of the ex-Soviet nation's President Serzh Sarkisian and the release of Sefilyan.
The lengthy standoff has shaken the tiny Caucasus republic and sparked clashes between police and protesters furious over the handling of the incident.
A fierce critic of the government, he was previously arrested in 2006 over calls for "a violent overthrow of the government" and jailed for 18 months. He was released in 2008.
Sarkisian, a pro-Russian former military officer, has been president of the country of 2.9 million people since winning a vote in 2008 that saw clashes between police and supporters of the defeated opposition candidate in which 10 people died.