Italy's President Sergio Mattarella has given the mandate to Foreign Secretary Paolo Gentiloni to try and form a new government.
Foreign Minister Mr Gentiloni was a key member of Matteo Renzi's Democratic Party.
Mr Renzi resigned on Wednesday after losing a referendum on constitutional reform on which he had staked his job.
Mr Gentiloni said he would try to form the government as soon as possible and that it would move "within the same framework" as Mr Renzi's.
"I am aware of the urgent need to give Italy a government with full powers," he said.