The leader of Estonia's largest political party received a formal request from the president on Friday to form a government, but quickly she downplayed her prospects of becoming prime minister.
Kaja Kallas, head of the centre-right Reform, pulled off a surprise win over the centre-left government in a March 3 vote for parliament, but fell short of a majority.
While she won backing in coalition talks with the Social Democrats, she failed to also win support from the Fatherland party in Estonia's fragmented 101-member assembly.
"I recognise I might not have enough support in parliament," Kallas said in a statement.
Centre Party Prime Minister Juri Ratas on March 11 invited the far-right EKRE to coalition talks, reversing a promise to block the anti-immigration party from the cabinet, and is expected to announce his own three-party coalition this weekend.
Still, Kallas said Reform and the Social Democrats, which together have 44 seats in parliament, would seek support from individual members of the Centre and the Fatherland parties, some of whom oppose Ratas' plan to tie up with the far right.
Kallas now has two weeks to present a plan for forming a cabinet. If she fails, President Kersti Kaljulaid can turn to Ratas who has worked for weeks on his alternative.
Populist parties have won ground across Europe ahead of elections in May to the European Parliament.
EKRE, whose fiercely anti-immigrant message lifted its support during the European migration crisis in 2015, got 19 seats in the March 3 vote, more than double the number from the previous election, winning broad support in rural areas.
Its leaders have promised street unrest if they were left out of the cabinet.