The musician, who has earlier expressed support for protests in Armenia, arrived in Yerevan earlier in the day.
"On our way back [from the airport] I tried to convince Serj Tankian to move to Armenia. He promised to reflect on it," Pashinyan said during a rally in central Yerevan.
Under Armenian law, the parliament has to elect prime minister in a week, or else it will be automatically dissolved. The country's new prime minister is now set to be elected on Tuesday, with Pashinyan renominated for the post.
The protests in Armenia began in mid-April as the opposition saw former President Serzh Sargsyan's nomination for the position of the prime minister after his two presidential terms as an attempt to hold on to power. Soon afterward, Sargsyan stepped down, with Armenian First Deputy Prime Minister Karen Karapetyan assuming the position of acting prime minister. However, rallies in the country continued as the opposition demanded an interim prime minister who will not be from the ruling Republican Party of Armenia (RPA).