Social Democrat Party (SDE) board members are calling on MPs to support Alar Karis as president at the second vote on Tuesday.
On Tuesday morning both former presidential candidate and current MEP Marina Kaljurand and MP Jevgeni Ossinovski told the media the party should support Karis.
Until now, the party supported current President Kersti Kaljulaid but she does not have enough support to be put forward as a candidate for a second term.
Speaking on ETV's morning show "Terevisioon", Ossinovski called on party members to support Karis' candidacy.
"After yesterday's vote, it is clear that Kersti Kaljulaid will not be president for a second term, and I think that in the situation we are in today, we need to support Alar Karis. In this new situation, I ask for support for him from my group. I hope that the president will be elected today. I think that there are no Social Democrats who do not support Karis in principle," Ossinovski said.
"The issue is not with Karis, but in our opinion, Kaljulaid did her job well and deserved another term," Ossinovski added.
The SDE will meet Karis on Tuesday morning to discuss Karis' candidacy.
Kaljurand, who stood as a candidate in 2016, also commented on the election on Tuesday morning. "Since I have been asked a lot about it in recent days, I will answer - if I could, I would vote for Alar Karis in the Riigikogu today," she said.
As an MEP and not a member of the Riigikogu, Kaljurand cannot vote to elect the president of Estonia.
"Vote as you see fit, each one of you! Vote so you are not embarrassed the next day. Because you have the mandate of the people and you are free in your decisions. Because the presidential election is more than "X" voting for or against a law in the Riigikogu," she said.
Yesterday it was reported SDE members did not vote for Karis on Tuesday because they did not know much about him or how he sees the role of president.
Karis, the director of the Estonian National Museum, was proposed as a candidate by the coalition parties Center and Reform two weeks ago. Smaller opposition parties SDE and Isamaa were not consulted even though cross-party support is needed to elect the president.
Yesterday, Karis received 63 votes in the first round but needed 68 to be elected.
Center and Reform have 59 votes between themselves, Isamaa 12 and SDE 11. However, two members - one from Reform and one from Isamaa - are unlikely to vote as they are both in hospital.
Editor: Helen Wright