He added that invites Karapetyan at noon today for talks in the hotel Marriott.
Despite winning two landslide presidential victories before becoming prime minister, Sargsyan was unpopular because of the perceived nepotism and corruption of his inner circle.
Russian Federation is a close ally of Armenia, a former Soviet republic.
Protest leader and parliament member, Nikol Pashinyan, whose liberal Way Out Alliance comprises a small minority in the legislature, is likely to be a candidate. "If the people's will is reflected in the voting, this election will be legitimate".
Negotiations over a transfer of power between the Armenian government and opposition broke down April 24, renewing the political crisis in the country and again sending tens of thousands of protesters out on to the streets.
According to him, the sides also touched upon Nagorno-Karabakh conflict.
There was widespread disagreement of the people, who for 12 days and led by dissenting representatives Nikol Pashinian, took to the streets day and night in Yerevan and different cities of the interior of Armenia to the cry of "take the step, reject Sergig" (Serg diminutive).
Later on Wednesday, the ruling Republican Party of Armenia declared it is ready to discuss any issue with all the parties. But to be elected, he will need the backing of at least six HHK lawmakers as well as the support of all opposition deputies.
Several Dashnaktsutyun lawmakers publicly expressed support for Pashinian and the street protests he has been leading for the past two weeks.
"Armenia is starting a new chapter in its history", Armenian President Armen Sarkissian said in a statement.
On Wednesday, Russia's ambassador to Yerevan met with Pashinian.
Sergei Lavrov, the Russian foreign minister, held talks in Moscow on Thursday with his Armenian counterpart, Eduard Nalbandian, Russia's foreign ministry said.
"What does "people's candidate" mean?" he told a news conference. Separately, Kremlin spokesman Dmitry Peskov told reporters that the political transition is "our Armenian friends' business" and said the Kremlin is "pleased that the situation is not moving toward a destabilization".
"We are open for discussing any issues: there is no closed agenda for us".
"The head has been chopped off", he said, referring to Sarkisian's resignation Monday, "but the body - the Republican Party - remains and it needs to be removed".
"This process took place entirely before your eyes".
He earlier told supporters he needed to become the next leader to oversee snap parliamentary elections and clean up the political system. "My goal is bring real changes to Armenia".
The fact that the current acting Prime Minister Karen Karapetyan is an old ally of Sargsyan and thus, is part of the governing group explains Russia's current aloofness.
"Don't get me wrong", he said.
However, the casually dressed Pashinian also explicitly threatened the ruling elite that he would call on the crowds to "blockade" the parliamentary buildings if HHK attempted to nominate one of their own as prime minister, which could lead to violence.