Hundreds of students started to march in Yerevan, waving flags and shouting "Nikol - prime minister!", while drivers sounded their car horns in support. Protesters also blocked several cross-roads in the city centre.
Police tried to persuade protesters to open roads, but did not use force.
Nikol Pashinyan, has called for a nationwide campaign of civil disobedience.
After a day of debate in parliament, the ruling Republican Party thwarted Pashinyan's bid to take over as prime minister on Tuesday. Legislators voted 45 in favour to 55 against. Under Armenia's constitution, a second vote for prime minister must be held in seven days' time. If again no candidate is elected, then parliament is dissolved.
Between 30,000 and 40,000 people gathered at Republic Square in Yerevan to follow the parliamentary session on large television screens.
Pashinyan, 42, has led weeks of anti-government rallies that forced former PM Serzh Sargsyan to resign.
He had earlier warned MPs of a "political tsunami" if they did not back him.
