The referendums are due to take place on Sunday and millions of ballot papers have been prepared.
Mr Putin has said putting off the vote could help create the conditions necessary for dialogue.
In what appeared to be a shift in Russian policy, Mr Putin also said this month`s presidential elections in Ukraine were a move "in the right direction".
His remarks came days after his spokesman said holding such an election would be absurd.
Moscow has vowed to protect the rights of the largely Russian-speaking people in the south and east against what it calls an undemocratic government in Kiev.
Ukraine`s interim authorities have rejected pro-Russian activists` demands for greater autonomy and sent in troops to seize back official buildings occupied by rebels.
"We respect Putin`s stance," said Denis Pushilin, a pro-Russian leader in the eastern city of Donetsk.
"He is a balanced politician. Therefore we will submit his proposal to the people`s council."
In Luhansk, a statement from pro-Russian groups quoted by Russian news agency Ria Novosti said: "We are putting this forward for discussion by all the people because Putin has appealed to supporters of federalisation, therefore a decision will be for all the people of Luhansk."
The White House said the "illegitimate, illegal" vote should be cancelled rather than postponed.
And Ukrainian interim Prime Minister Arseniy Yatseniuk dismissed Mr Putin`s calls as "hot air".
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