Russia has two military bases in the ex-Soviet republic, and Russian President Vladimir Putin spoke to Armenian President Armen Sarkissian by phone on Wednesday.
The Russian embassy in Yerevan said Wednesday that its officials had met with Pashinyan.
Pashinian and his supporters are demanding that parliament choose a "people's candidate" who is not from the ruling Republican Party for the role of prime minister.
Sargsyan resigned on Monday, following days of protests in Yerevan against his government, which critics accuse of corruption and authoritarian rule. "The opposition movement should do everything in its power to enable the process to bring about a real change".
The Yelk opposition bloc nominated Pashinyan for prime minister, but he was 13 votes short of a majority on Wednesday. A candidate would need 53 votes to get elected. They want a sweeping political reconfiguration before ending their protests, which continued on Thursday.
"If the Republicans do not want to leave themselves, we will force them", Anna Mkrtchyan, a 38-year-old hairdresser, told AFP in central Yerevan. A day after Sargsyan stepped down, the country's opposition called for a meeting with the caretaker prime minister to discuss a "peaceful transfer of power".
Pashinyan called a temporary halt to protests across the country and said he was willing to hold talks with acting head of government Karen Karapetyan on Friday in front of journalists.
But police later abandoned efforts to clear streets in the centre, saying it could not take sides in a political crisis.
Meanwhile, President Armen Sarkisian said on April 26 that the country was experiencing a "new page" in its history.
Denying this reality would be a political shortsightedness.