The father and stepmother of the two boys found dead in a car on Sunday in Xylophagou were on Monday remanded for three days pending investigations into the circumstances of their death.
The police had requested four-day remand orders, however the British bases court judge issued three-day remands with the possibility of renewing further if necessary.
The remand orders were issued as the judge said the suspects could move outside the British bases or flee to the occupied north.
The police now have until Thursday at midday to conclude their investigations.
The two boys, aged eight and ten, are believed to have been playing when they locked themselves in the vehicle and appear to have suffocated and sustained burns from exposure to the sun.
The father and stepmother, 30 and 38 respectively, who were at work at the time the children died, were arrested by the British bases police on suspicion of negligence.
The bases police had been notified by a civilian that there were two children apparently unconscious in a vehicle.
Rescue crews had to break the car windows to get to the children.
The boys were taken by ambulance to hospital, where doctors confirmed their death.
According to Reporter, Xylophafou community leader Giorgos Ioulianos said the children had arrived on the island to visit their parents who are working in Cyprus.
Earlier reports suggested the father and stepmother had left the children in the car to sleep while they were at work.
Police investigations are under way.
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