The order - circulated to the Iraqi army, border guard forces, Red Crescent and other government officials – said preparations should be made to receive Syrians "whose extraordinary conditions in their country oblige them to change location," a statement from Maliki's office said.
General Issam Yassim, a senior border commander, told Reuters at Iraq's southern Al-Waleed border crossing with Syria, 560 km (347 miles) west of Baghdad, that he had received the directive.
"The order came 30 minutes ago," he said, adding that it applied to all Iraqi border crossings with Syria.
Al-Waleed, one of Iraq's three main border crossings with Syria, is held by Syrian government forces and has been the main crossing point for Iraqis fleeing the violence in Syria, especially from Damascus.
Syrian rebels say they control another crossing, at Albu Kamal-Qaim, based on a major trade route further north. It was sealed by the Iraqi army due to government fears that the violence in Syria could spill across the border.
A third crossing at Rabia, near the northern Iraqi city of Mosul, passed briefly into rebel hands, but is now under the control of Syrian government forces.
There is another crossing in Iraqi Kurdistan, near the Turkish border.
Thousands of Iraqis have already returned home due to the turmoil in Syria but face sectarian violence at home. At least 89 people were killed in gun and bomb attacks against mostly Shia Muslim targets on Monday.
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The spillover effect has reached Iraq, which sees an escalation of sectarian violence due to the fightings in Syria. Many Shia Iraqis fled their country during the civil war and took refuge in Assad's kingdom. Since the outbreak of conflicts in Syria, they feel unsafe and return to Iraq, just to find themselves in another inferno.