Prime Minister Nikol Pashinyan has faced fierce criticism over his handling of last year's war with Azerbaijan, which many see as a national humiliation. On Thursday, military general staff joined calls for him to step down.
Armenian President Armen Sarkissian has said that he had refused to sign a prime ministerial order to dismiss the army's chief of staff, deepening a national political crisis.
The ex-Soviet nation has faced turmoil since Prime Minister Nikol Pashinyan signed a Moscow-brokered peace accord in November, sealing a humiliating defeat to Azerbaijan after six weeks of fighting over the disputed Nagorno-Karabakh region.
Divisions widened on Thursday when Pashinyan defied a call by the military to resign, accused the army of an attempted coup, and ordered the chief of the general staff Onik Gasparyan to be fired.
On Saturday, Armenian President Sarkissian said in a statement that he would not back the sacking.
"The president of the republic, within the framework of his constitutional powers, returned the draft decree with objections," the presidency said.
It added that the political crisis "cannot be resolved through frequent personnel changes".
Earlier in the day, 5,000 opposition protesters waving Armenian flags and calling for Pashinyan's resignation gathered for the third day running outside the parliament in Yerevan.
Some protesters have now set up camp there.
"Today Pashinyan has no support. I call on the security services and the police to join the army, to support the army," said former premier Vazgen Manukyan, who has been named by the opposition to replace Pashinyan.
"I am sure that the situation will be resolved within two to three days," he told the crowd.
Pashinyan has faced fierce criticism since he signed a peace deal over Nagorno-Karabakh, an ethnic Armenian region that broke from Azerbaijan's control during a war in the early 1990s.
The agreement was seen as a national humiliation for many in Armenia, but Pashinyan has said he had no choice but to agree or see his country's forces suffer even bigger losses.