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 February 12 agreements signed in Minsk, brokered by France and Germany.
The exchange came as 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 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 February 22, 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, according to the UN.
This followed Russia’s annexation of Ukraine’s southern Crimea peninsula.
Gen. Alexander Lentsov, a Russian member of the Joint Centre for Control and Co-operation (JCCC), said: “We have designated February 22 as <<D-Day>> as determined by the agreement from all sides. So from tomorrow [February 22] 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.
Petro Kanonik, a Ukrainian member of the JCCC, said Kiev had been informed of the rebel move, according to Ukraine’s Ukrainska Pravda website.
The pullout process had been due to start on February 17 and completed by March 3, but Gen. Alexander Lentsov said it would now take until March 7.
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 February 21.
Yesterday, Ukraine’s military and the rebels completed the first exchange of prisoners after the ceasefire. A total of 139 Ukrainian soldiers were freed and 52 rebels.
Ukrainian President Petro Poroshenko tweeted the news of the prisoner exchange, which took place near the front line town of Zholobok.
Some of the government soldiers were wounded and walking on crutches.
Petro Poroshenko originally said 140 soldiers would be freed, and Ukrainian officials said one more soldier would be released in the coming days.
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