Prime Minister Najib Razak also said that as part of an agreement he reached by phone with rebel leader Alexander Borodai this evening, independent international investigators will be given "safe access" to the site where the Malaysia Airlines jet went down in eastern Ukraine en route from Amsterdam to Kuala Lumpur on Thursday, killing all 298 people onboard.
Najib said that as part of the agreement, the black boxes would be handed over to the Malaysian team in Donetsk at 9 pm today Ukraine time.
From there, they will be flown to Amsterdam on a Dutch C130 Hercules military plane and handed over to Dutch authorities.
"I must stress that although an agreement has been reached, there remain a number of steps required before it is completed," Najib said at a hastily arranged news conference at his residence just after midnight today.
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"There is work still to be done, work which relies on continued communication in good faith. Mr. Borodai and his people have so far given their cooperation."
Yesterday, Najib had said that the remains of the Malaysian victims must be returned to Malaysia before the Eid al-Fitr, which marks the end of the Muslim fasting month of Ramadan. This year, it falls on July 28.
Anger and resentment toward the Russian-backed rebels and Moscow have been escalating worldwide, including in Malaysia, where there have been calls for economic sanctions against Russia.