The gunmen seized the compound five days ago and have been demanding the release of an opposition leader arrested last month on weapons charges.
Supporters of the gunmen have staged rallies nearby and clashed on Wednesday with police, who fired tear gas.
Mr Sarkisian urged the gunmen to "sober up" and end their "provocative" action.
In comments reported by Armenian Armenpress news agency, he said: "No problem will be solved in Armenia with the use of force, raids and hostage-taking. The resolution of the problem will be an important test for Armenia and the maturity of our society."
Mr Sarkisian said the government would act "in line with Armenia's laws" if the gunmen persisted, but he gave no further details.
The hostage-takers have been demanding the release of Jirair Sefilian, a military veteran of Armenia's conflict in Nagorno-Karabakh, who has been accused of illegally possessing weapons and preparing to seize government buildings.
In taking control of the police station in Armenia's capital on Sunday, the gunmen killed one police officer and injured two others. They later released five hostages.
Those still being held include a deputy police chief.
Mr Sefilian has criticised Mr Sarkisian over his handling of the conflict involving pro-Armenian separatists in the Nagorno-Karabakh region.
Nagorno-Karabakh lies within Azerbaijan but has an ethnic Armenian majority. A bloody war erupted after the end of Soviet rule in 1988, and there has been frequent unrest since, the latest in April, when clashes left dozens dead.
Armenia's President Serge Sarkisian has urged gunmen holding four hostages at a police station in Yerevan to free their captives and lay down their arms.