The consultations were earlier planned for Sunday, after which the president could announce a candidate for prime minister, according to Aleksandr Zhukov, First Vice-Speaker of the State Duma, the lower house of parliament, who is seen as the most possible candidate for the post.
President Putin held maiden discussions on a future government with the parliamentary majority leaders on Wednesday, February 25.
Mr Putin himself has spoken out in favor of holding discussions on issues related to the formation of a new government with the parliament.
"In the state of the union address I said that such issues were to be resolved by means of consultations with the parliamentary majority," the president said at a meeting with the members of the sacked cabinet on Wednesday.
This may add uncertainty and require certain effort and time, admitted the president.
However, the head of state said the Duma would hopefully approve the candidature of a new premier in the near future.
Vladimir Putin dismissed the government on Tuesday, February 24 and appointed Viktor Khristenko acting prime minister. In a relevant decree, the president ruled that the cabinet members should continue performing their duties unit a new cabinet is formed.
According to article 111 of the Constitution, candidatures for the post of premier must be advanced within two weeks since the dismissal or resignation of the government.
The State Duma is to approve or decline the president-advanced candidature within a week.