Speaking at Thursday's regular Thursday cabinet press conference, Kallas noted that under the relevant legislation, potential candidates have up until four days before the election to be registered.

"There's time left until then," Kallas said. Since the opening rounds of the process start at the end of August, that leaves nearly three months for candidates to declare.

While Reform were in opposition, until January this year, they would have been expected to have backed Kersti Kaljulaid for a second consecutive term. However, since entering office with Center, the picture is less clear since former prime minister and Center leader Jüri Ratas has been widely tipped for a potential bid.

Ratas has not declared, nor has his party put up any candidate, and similarly, Kallas' Reform Party have not yet stated publicly who they would/wouldn't back, though an anonymous Reform Party source recently told daily Postimees that the party does not favor a second term for Kersti Kaljulaid.

Kallas added that she has been trying to reach a compromise with Center, adding that her party has had the initiative at all times, hence Center looking for a candidate with a broad base of support.

Talks are also underway with the opposition parties, she said, to get as broad a level of support as possible.

In any case, a candidate would need two thirds of the Riigikogu's 101 MPs to vote in favor of it, i.e. 67 votes. Candidates also need at least 21 votes to be able to run in the first place.

Reform and Center have 59 seats between them, meaning that assuming all their MPs voted in favor of a joint candidate, they would still require 7 more votes from any of the three opposition parties – the Social Democrats (SDE), Isamaa or the Conservative People's Party of Estonia (EKRE). Henn Põlluaas, former Riigikogu speaker, is in fact the only political figure to have declared themselves a candidate so far, along with academic Tarmo Soomere.

"We are trying to avoid the mistakes that were made last time," Kallas said.

"We are trying to find a candidate who could get the required support in the Riigikogu or the electoral college," she went on, noting that a president who was not decided by an election was not a desirable state of affairs.

In 2016, after several inconclusive rounds at both Riigikogu and in the electoral colleges, Kersti Kaljulaid, who had been working for the European Court of Auditors in Luxembourg up until that time, was voted in by a Riigikogu council of elders, comprising Riigikogu speaker and deputy speakers, and the party group leaders of each of the five represented parties.

Jüri Ratas himself is currently Riigikogu speaker.

In 2016, Marina Kaljurand, Siim Kallas, Mailis Reps, Eiki Nestor, Mart Helme and Alar Jõks between them failed to get a majority with Riigikogu or electoral college.

Kiik: No need to hurry process

Health minister and Center Party member Tanel Kiik, also appearing at Thursday's press conference, said that he, too, thought there was no need to rush

Noting that the two coalition parties need other parties' MP's votes as well, Kiik said that: "This is why consultations are underway."

Kiik also agreed resolution in the Riigikogu was the best option, and said that the majority of MPs felt that way.

The local elections take place on October 17 – if the presidential electoral process was a protracted as it was in 2016 (when there were no other elections taking place), the two elections could clash.

Presidential candidates also need to be Estonian citizens by birth, and at least 40 years of age. No more than two consecutive, five-year terms are permitted, though additional non-consecutive terms are allowed. Two presidents have served for two consecutive terms so far since the restoration of Estonian independence: Lennart Meri and Toomas Hendrik Ilves.

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