"We suggest that we should hold a snap election and, if the people support him [Pashinyan], he will run [in the election] … A candidate from the people can [only] be determined during an election," Karapetyan told reporters.
He added that he did not know of such a country where a "candidate from the people" could be elected on the street.
Earlier in the day, Karapetyan said that the second round of his talks with opposition leader Nikol Pashinyan, scheduled for Wednesday, had been canceled over new unilateral demands for the format of the talks made by the opposition figure.
On Monday, Sargsyan resigned amid large-scale anti-government protests against his appointment. Following Sargsyan's resignation, First Deputy Prime Minister Karapetyan became acting prime minister and entered negotiations with the protest leader, Pashinyan.
Sargsyan served two consecutive five-year terms as president until April 9. His election as prime minister on April 17 was largely regarded as an attempt to get around presidential term limits, since the 2015 constitutional amendments transferred governing powers from the president to the head of the government, and provoked mass protests.