Timofti made the announcement after consultations with the leaders of parliamentary factions.
The president said he would sign the nomination decree later on April 10.
Filat's pro-Western government resigned on March 8, after losing a no-confidence vote in parliament on March 5.
The opposition Communists had called for the no-confidence vote amid allegations of corruption in the government.
"I regret that the parties of the former Alliance [for European Integration] have not succeeded so far in forming a new pro-European majority in parliament," Filat said. "But I believe that the existing potential in that regard has not been exhausted yet."
Filat will now attempt to form a government. If this process fails to produce a cabinet with majority support in parliament three times within 45 days, the president will dismiss the parliament and call early legislative elections.