More than 14,000 people have signed an online petition calling for Kersti Kaljulaid to continue as president.
The petition, posted on the Rahvaalgatus portal, was started on August 23 by Entrepreneur Peedu Tuisk.
Some of the reasons given for Kaljulaid's continuation are that she has successfully fulfilled her role president, led Estonia's successful campaign for temporary membership of the UN Security Council, been active in foreign policy and supported socially important campaigns and initiatives.
Three initiatives against Kaljulaid continuing have also been created on the Rahvaalgatus website, one by EKRE Member of European Parliament Jaak Madison. The initiatives are public discussions rather than petitions which cannot currently be signed.
The majority of active petitions on the website have been signed by under 1,000 people. An ID card is needed to give a signature.
Kaljulaid has not been put forward as a presidential candidate for the first round of voting on Monday as only the Social Democratic Party has said it would support her bid. The party has 11 members in the Riigikogu but needs 21 signatures from members to nominate her.
The Center, Isamaa and EKRE parties have said they will not support Kaljualid for a second term. The Reform Party agreed to when it was in opposition but now wants to nominate a candidate with cross-party support. Sixty-eight members must support a candidate for them to become president.
If the first round of voting fails to elect a candidate, Kaljulaid could be nominated forward in subsequent rounds. She is eligible to run for a second five-year term.
Editor: Helen Wright