The decision was welcomed by Kiev's pro-EU leadership and the Kremlin -- one of the few times the ex-Soviet neighbours have agreed on anything since the conflict erupted last year.
The European Union also called the concessionary move a "fundamental step" toward peace.
The change in rebel rhetoric coincided with the withdrawal of Ukrainian tanks from the demarcation line in one of the two separatist eastern industrial provinces.
The chief negotiators of the self-proclaimed "people's republics" said they had "agreed to postpone the (Donetsk) elections of October 18 and the (Lugansk) poll of November 1 until next year."
That meeting ended with French President Francois Hollande declaring that the rebels could not possibly organise internationally legitimate elections within such a short timeframe.
Poroshenko has also called the votes "fake" and demanded their cancellation.
Ukrainian officials said yesterday that Hollande and German Chancellor Angela Merkel had put strong pressure on Putin -- who denies any involvement in the fighting -- to convince the militia command to delay their vote.
The two met today in the Belarussian capital Minsk -- the same location where Putin and Poroshenko agreed in February to find a way out of one of Europe's bloodiest conflicts since the Balkans wars of the 1990s.
The insurgents did not say when they now intended to hold their polls.
But they pressed a series of demands that will be tough for Poroshenko to push through a Ukrainian parliament where nationalist forces play an important role.
