The NSS said its former head Artur Vanetsyan, the former head of the Republican Party parliamentary faction Vahram Baghdasaryan and war volunteer Ashot Minasyan were under arrest.
"The suspects were planning to illegally usurp power by murdering the prime minister and there were already potential candidates being discussed to replace him," said the NSS in a statement.
Pashinyan had come under pressure in recent days, with thousands of demonstrators protesting since Tuesday and demanding he step down over a ceasefire that secured territorial advances for Azerbaijan in the disputed region of Nagorno-Karabakh after six weeks of intense fighting.
The ceasefire halted military action in and around Nagorno-Karabakh, an enclave internationally recognized as part of Azerbaijan but populated by ethnic Armenians.
On Saturday, ethnic Armenian villagers in Karabakh set their houses on fire before fleeing to Armenia on the eve of a deadline that will see parts of the territory handed over to Azerbaijan as part of the ceasefire agreement.