Gen Alexander Lentsov said the pro-Russian rebels had signed the orders to complete the withdrawal over the next two weeks, starting from Sunday.
It is not clear whether the move will be reciprocated by Ukraine.
This comes as Ukraine and the separatists exchanged 191 prisoners, a key part of the Minsk ceasefire deal.
It was the first step carried out successfully under the terms of the February15 agreements signed in the Belarusian capital, brokered by France and Germany.
The exchange came as US Secretary of State John Kerry said Washington was considering “serious sanctions” against Russia following breaches of the truce, and that a decision would be made in the coming days.
Kremlin’s spokesman Dmitry Peskov said sanctions would not help solve Ukraine’s crisis.
Meanwhile, thousands of Ukrainians – as well as a number of European leaders – are expected to take part in a “dignity march” in the capital Kiev on Sunday, remembering the victims of sniper fire during protests last February.
Nearly 5,700 people have died since the fighting erupted last April Ukraine’s Eastern Donetsk and Luhansk regions.
Gen Lentsov, a Russian member of the Joint Centre for Control and Co-operation (JCCC), said: “We have designated February 22 the “D-Day” as determined by the agreement from all sides. So from Sunday we will within the period of 14 days observe the agreement on the pullback of heavy weapons.”
He said the leaders of the self-proclaimed rebel Luhansk and Donetsk people’s republics had already signed the orders.
“We hope for Kiev’s participation and help first and foremost,” the general added.
The pullout process had been due to start last Tuesday and completed by March 3, but Gen Lentsov said it would now be March7.
Ukraine and rebel forces accuse each other of multiple breaches of the truce, and there were reports of violations around Donetsk and the port city of Mariupol on Saturday.
The rebels took the strategic transport hub of Debaltseve during the week in spite of the ceasefire, arguing the truce did not apply to the flashpoint town, forcing government troops to retreat.