Meri was trying to patch together what will be Estonia's third government since the tiny Baltic state regained its independence in 1991 after 50 years as part of the former Soviet Union.
Newspapers predicted a period of drawn-out talks although Meri's office said he did not want to delay.
"The president will have meetings with different parties and is trying to find a new prime minister as quickly as possible," said a spokeswoman for Meri.
The seven-month-old coalition led by Prime Minister Tiit Vahi collapsed Wednesday after he resigned in the wake of a scandal over secret recordings made by former interior minister Edgar Savisaar. The scandal over the tapes caused a major row between the main ruling group, the Coalition Party, and the Centrist Party, of which Savisaar was leader.
The coalition, which included the Rural Union as third party, commanded 57 seats in the 101-seat parliament.
Savisaar was sacked before Vahi quit, but the premier said he had to resign to protect Estonia's image.
Meri's spokeswoman said the president would have two sets of meetings with political parties and said a decision on a candidate for prime minister should come soon. Meri has two chances to nominate a candidate and if neither of these is able to form a government, then parliament chooses a new premier.
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